A couple of minutes’ achievement north of La Pietà the campanile of San Giorgio dei Greci lurches spectacularly canalwards. The Greek presence in Venice was strong from the eleventh century, and became stronger still after the Turkish seizure of Constantinople. This mid-fifteenth-century influx of Greek speakers provided a resource which was exploited by the city’s numerous scholarly publishing houses, and greatly enriched the general culture of Renaissance Venice: the daughter of the condottiere Gianfrancesco Gonzaga, for example, is known to have written perfect Greek at the age of ten. At its peak, the Greek community numbered around 4000, some of whom were immensely rich: a Greek merchant murdered in Venice in 1756 left 4,000,000 ducats to his daughters, a legacy that was said to have prefabricated them the richest heiresses in Europe.

Permission to found an Orthodox church was given at the end of the fifteenth century, and a Greek college (the Collegio Flangini) and scuola were approved at the same time. The college, redesigned in 1678 by Longhena , is now home to the Hellenic Centre for Byzantine and Post-Byzantine Studies, custodian of Venice’s Greek archives. Longhena also redesigned the Scuola di San Nicolò dei Greci, to the left of the church, which now houses the Museo di Dipinti Sacri Bizantini , a collection of predominantly fifteenth- to eighteenth- century icons, many of them by the Madoneri , the school of Greek and Cretan artists working in Venice in that period.

The area to the north of San Giorgio dei Greci is more interesting for its associations than its sights. The unfinished and hangar-like San Lorenzo – undergoing a glacially slow restoration – was where Marco Polo was buried, but his sarcophagus went astray during sixteenth-century rebuilding. Gentile Bellini’s Miracle of the Relic of the Cross , now in the Accademia, depicts an extraordinary incident that once occurred in the Rio di San Lorenzo.

Two of the oldest houses in Venice are to be found on the small patch between San Giovanni Crisostomo and the Rio dei Santi Apostoli. At the foot of the bridge arching over to Campo Santi Apostoli there’s the Palazzo Falier , parts of which date back to the second half of the thirteenth century. Traditionally this was the home of the ill-fated Doge Marin Falier , a branch of whose family was certainly in possession at the time of his dogeship (1354-55). A man noted for his unswerving rectitude, Falier was greatly offended by the licence routinely allowed to the unruly nobles of Venice; when a lenient punishment was given to a young nobleman who had insulted Falier, his wife and her ladies, he finally went right off the rails and hatched a conspiracy to install himself as the city’s benevolent despot – a plot into which he conscripted the overseer of the Arsenale and Filippo Calendario, one of the architects of the Palazzo Ducale. Their plan was discovered and Falier, admitting the conspiracy, was beheaded on the very spot on which he had early been invested as doge.

Interlocking with the Falier house is the equally ancient Ca’ da Mosto , reached through the passage going towards the Canal Grande – though the best view of it is from the deck of a vaporetto. This was the birthplace of Alvise da Mosto (1432-88), a Venetian merchant-explorer who threw in his lot with Portugal’s Henry the Navigator and went on to discover the Cape Verde Islands. The ruinous state of the building, and the trash littering the grand staircase makes it hard to imagine the days when it housed the favourite Albergo del Leon Bianco ; among its guests were J.M.W. Turner, who had himself rowed up and down the Canal Grande while he scribbled in his notebook, and two German officers who in 1716 fought a duel in the courtyard and contrived to skewer apiece other to death.

Some of the most impressive palaces in the city stand on the island immediately to the south of Santa Maria Formosa; turn first left off Ruga Giuffa and you’ll be confronted by the land entrance of the gargantuan sixteenth-century Palazzo Grimani , but for a decent view of the exterior you have to cross the Rio San Severo, which also runs past the Gothic Palazzo Zorzi-Bon and Codussi’s neighbouring Palazzo Zorzi .

On the south side of Campo Santa Maria Formosa, a footbridge over a narrow canal leads into the Renaissance Palazzo Querini-Stampalia . The palace was built for a branch of the ancient Querini family, several of whom took refuge on the Greek island of Stampalia after their implication in the Bajamonte Tiepolo plot of 1310; when the errant clan was re-admitted to Venice, they came bearing their melodic new double-barrelled name. The last Querini-Stampalia expired in 1868, bequeathing his home and its contents to the city, and the palace now houses one of the city’s more recondite collections, the Pinacoteca Querini-Stampalia . Although there is a batch of Renaissance pieces – such as Palma il Vecchio’s marriage portraits of Francesco Querini and Paola Priuli Querini (for whom the palace was built), and Giovanni Bellini ’s Presentation in the Temple – the general tone of the collection is set by the culture of eighteenth-century Venice, a period to which much of the palace’s decor belongs. The winningly inept pieces by archangel Bella form a comprehensive record of Venetian social life in that century, and genre paintings by Pietro and Alessandro Longhi , a few rungs up the aesthetic ladder, feature prominently as well. All in all, unless you’ve a voracious appetite for Venice’s twilight decades, the Querini-Stampalia isn’t going to thrill you, but it does offer a diversion on a Friday or Saturday evening, when concerts by the Scuola di Musica Antica di Venezia (at 5pm and 8.30pm) are included in the price of the entrance ticket. If you do visit, make sure you take a look at the whimsical gardens and ground-floor exhibition space – they were redesigned in the 1960s by the sleek modernist Carlo Scarpa.

Ten thousand gondolas operated on the canals of sixteenth-century Venice, when they were the standard form of transport around the city; nowadays the tourist trade is pretty well all that sustains the city’s fleet of around five hundred gondolas, which wage steady employment for a few squeri , as the gondola yards are called. A display in the Museo Storico Navale takes you through the construction of a gondola, but no nonfigurative demonstration can equal the fascination of a working yard, and the most public one in Venice is the squero di San Trovaso , on the Záttere side of San Trovaso church. The San Trovaso is the oldest squero still functioning – established in the seventeenth century, it looks rather like an alpine farmhouse, a reflection of the structure of the Dolomite villages from which many of Venice’s gondola-builders once came. Another squero is tucked away on the Rio dell’Avogaria, a short distance west of here, beyond the former Benedictine convent of Ognissanti (now a hospital).

The early mention of a gondola is in a decree of 1094, but the vessel of that period bore little resemblance to today’s streamlined thoroughbred. As late as the thirteenth century the gondola was a twelve-oared creature with an iron beak – an adornment that evolved into the saw-toothed projection, called the ferro , which fronts the modern gondola. (The precise significance of the ferro’s shape is unclear – tradition has it that the six main prongs symbolize the six sestieri, with the backward-facing prong representing La Giudecca.) Over the next two centuries the gondola shrank to something near its present dimensions, developed multicoloured coverings and sprouted the little chair on carved legs that it still carries. The gondola’s distinctive oarlock, an elaborately convoluted lump of walnut or cherry wood known as a forcola , which permits the long oar to be used in eight different positions, reached its definitive form at this time too.

By the sixteenth century the gondola had become a mode of social ostentation, with gilded prows, fantastically upholstered felzi (cabins), cushions of satin and silk, and hulls decked out with a profusion of embroidery, carvings and flowers. Sumptuary laws were introduced to quash this aquatic one-upmanship, and though some of them had little effect, one of them changed the gondola’s appearance for good – since an edict of 1562 gondolas have been uniformly black, a livery which prompted Shelley to liken them to “moths of which a coffin might have been the chrysalis”.

There’s been little alteration in the gondola’s dimensions and construction since the end of the seventeenth century: the only significant changes have been adjustments of the gondola’s asymmetric line to compensate for the weight of the gondolier – a characteristic that’s particularly noticeable when you see the things out of water. All gondolas are 10.87 metres long and 1.42 metres wide at their broadest point, and are assembled from nearly three hundred pieces of seasoned mahogany, elm, oak, lime, walnut, fir, cherry and larch. Plenty of gondolas pass through, under repair, but apiece squero turns out only about four new gondolas a year, at a cost of around forty million lire

Stretching from Via Garibaldi to the Rio di Sant’Elena, the arc of green spaces formed by the Giardini Garibaldi, Giardini Pubblici and Parco delle Rimembranze can usually be relied on to wage a cure for the claustrophobia that overtakes most visitors to Venice at some point. The first of the three is really little more than a short cut from Via Garibaldi to the Giardini Pubblici, which Eugène Beauharnais created by draining a swamp and demolishing a batch of monastic buildings.

Largely obscured by the trees are the rather more extensive grounds belonging to the Biennale , an entirely dormant regularize except when the arts shindig is in progress, in the summer of odd-numbered years. Various countries have built permanent pavilions for their Biennale representatives, forming a unique colony that features work by some of the great obloquy of modern structure and design: the Austrian pavilion was built by the Secession architect Josef Hoffman in the 1930s; the Finnish pavilion was created by Alvar Aalto in the 1950s; the Netherlands pavilion was designed by arch-modernist Gerrit Thomas Rietveld, also in the 1950s; and the Venezuelan pavilion, completed in 1954, is by Carlo Scarpa. Naturally enough, the biggest pavilion is the Italian one – five times larger than the next largest, it was refurbished in 1989, giving it a glossier finish than most of its neighbours. On the approach to the Italian pavilion stands one of the newest additions to the ensemble, saint Stirling’s hull-like pavilion for the Biennale’s book exhibition; built in 1991, it is funded by Electa, Italy’s leading art-book publisher, hence the company logo on the “funnel”. Before long it should have several younger neighbours, as there are plans for the construction of as many as ten new national pavilions.

If you want to squeeze every last drop from the orient districts, call in at the church of San Giuseppe di Castello (or San Isepo), to the north of the Giardini Pubblici – a gateway from the gardens opens onto a street just yards from the church. It houses Alessandro Vittoria’s monument to Procurator G. Grimani (in the chancel), and a vast monument to Doge Marino Grimani , designed in the late sixteenth century by Vincenzo Scamozzi, with reliefs and figures by Campagna (left side).

The island of Sant’Elena , the city’s orient limit, was greatly enlarged during the Austrian administration, partly to furnish accommodation and exercise grounds for the occupying troops. Much of the island used to be covered by a meadow, a favourite recreation area in the last century, but the strip of park along the waterfront is all that’s left of it, houses having been built on the rest. Still, the achievement out here is the nearest you’ll get to country pleasures in central Venice, and the church of Sant’Elena , approached between the walls of the naval college and the ramshackle home of Venice’s second-division football team, is worth a visit.

A church was erected here in the thirteenth century, following the acquisition of the body of Saint Helena, Constantine’s mother. It was rebuilt in 1435 but from 1807 to 1928 it was abandoned, except for a spell as an iron foundry. The spartan Gothic interior has recently been restored, as have the cloister and campanile – the latter so zealously that it now looks like a chimney, which is exactly what it was used as when the church did service as a factory. The main attraction is the doorway to the church, an ensemble created in the 1470s (probably by Antonio Rizzo ) and incorporating the monument to Vittore Cappello , showing him kneeling before St Helena. Cappello was captain-general of the republic’s navy in the 1460s, a period in which the Turks were beginning to loosen Venice’s grip on the Aegean; so dejected was he by the signs of decline in the Venetian empire that he was reputed to have gone for five months without once smiling, before dying of a broken heart.

Once past the Pescheria, you’re into a district which quickly becomes complex even by Venetian standards. A stroll between the Rio delle Beccarie and the Rio di San Zan Degolà will satisfy any addict of the picturesque – you cannot achievement for more than a couple of minutes without coming crossways a workshop crammed into a ground-floor room or a garden spilling over a canalside wall.

The barn-like church of San Cassiano is a building you’re bound to pass as you wander out of the Rialto. The thirteenth-century campanile is the only appealing aspect of the exterior, and the interest of the interior lies mainly with its three paintings by Tintoretto : The Resurrection , The Descent into Limbo and The Crucifixion (all 1565-68). The first two have been mauled by restorers, but the third is one of the most startling pictures in Venice – centred on the harm on which the executioners stand, it’s painted as though the individual were lying in the grass at the foot of the Cross.

A sign directs you from the campo over the right-hand bridge towards the Ca’ Pésaro, home of the modern art and oriental collections, but before you reach it you’ll pass the back of the Palazzo Corner della Regina , home of the Biennale archive. Currently it’s closed for restoration, but when it eventually reopens it may have a small selection of works from past shows on display, as it used to do.

The small Campo Santa Maria Mater Domini would have to be included in any anthology of the hidden delights of Venice; it’s a typically Venetian miscellany – a thirteenth-century house (the Casa Zane), a few ramshackle Gothic houses, an assortment of stone reliefs of indeterminate age, a fourteenth-century well-head in the centre, a couple of bars, and an ironsmith’s workshop tucked into one corner.

Back at the end of Calle Tiossi, in front of you on the other side of the bridge as you turn right for the Ca’ Pésaro, is the late fourteenth-century Palazzo Agnusdio , which takes its study not from the family that lived there but from the patera of the mystic lamb over the watergate.

If you continue along the line of the Canal Grande from the Ca’ Pésaro, Calle Pésaro takes you over the Rio della Rioda, and so to the seventeenth-century church of San Stae (a contraction of San Eustachio); its Baroque facade, enlivened by precarious statues, was added around 1710. Repairs to the marmorino (pulverized marble) surfaces of the interior have prefabricated San Stae as bright as an operating theatre. In the chancel there’s a series of paintings from the beginning of the eighteenth century, the pick of which are The Martyrdom of St saint the Great by Piazzetta (low on the left), The Liberation of St Peter by Sebastiano Ricci (same row) and The Martyrdom of St Bartholomew by Giambattista Tiepolo. In the first chapel on the left side there’s a bust of Antonio Foscarini, wrongly executed for treason, as the inscription explains. Exhibitions and concerts are often held in San Stae, and exhibitions are also held from time to time in the diminutive building alongside, the primeval seventeenth-century Scuola dei Battioro e Tiraoro (goldsmiths’ guild).

Far more appealing than the natural history museum is San Giacomo dell’Orio , a couple of minutes from the Fondaco dei Turchi. Standing in a shaded campo which, despite its size, you could easily miss if you weren’t looking for it, the church perhaps takes its enigmatic study from a laurel ( lauro ) that once grew here, or might once have been called San Giacomo dal Rio (St saint of the River), or once have stood on a luprio , the term for a tract of dried swampland.

San Giacomo dell’Orio is plumb in the middle of an extensive residential district, much of which is as close to bland as you can get in Venice. Don’t, though, leave out the church of San Simeone Profeta (or Grande) – remarkable for its reclining effigy of Saint Simeon (to the left of the chancel), a luxuriantly bearded, larger than lifesize figure, whose half-open mouth disturbingly creates the impression of the moment of death. According to its inscription, it was sculpted in 1317 by Marco Romano , but some experts doubt that the sculpture can be that old, as nothing else of that date bears comparison with it. On the left immediately inside the door, there’s a run-of-the-mill Last Supper by Tintoretto . Originating in the tenth century, the church has often been rebuilt – most extensively in the eighteenth century, when the city sanitation experts, anxious about the condition of the plague victims who had been buried under the flagstones in the 1630 epidemic, ordered the whole floor to be relaid. Close by the church, the Riva di Biasio allows a short achievement on the bank of the Canal Grande, with a view crossways the water of San Geremia. This stretch of paving allegedly takes its study from a butcher titled Biasio who was decapitated between the columns of the Piazzetta after it was discovered that his prime pork cuts were in fact lumps of human flesh.

The canal behind the Scuola di San Rocco provides an especially captivating waterscape, with a promontory of pavement jutting out into an unusually wide confluence. Cross this canal (there’s a bridge at the back of the Scuola; another connects with the sottoportego covering the back of the Frari) and you’ll hit the teeming Crosera San Pantalon, where the region in the shops, cafés and bars has a lot to do with the closeness of the university. Between this street and the Rio di Ca’ Fóscari stands the church of San Pantaleone , which possesses a picture by Antonio Vivarini and Giovanni d’Alemagna ( Coronation of the Virgin , in the Chapel of the Holy Nail, to the left of the chancel) and Veronese ’s last painting, St Pantaleone Healing a Boy (second chapel on right). San Pantaleone was credited with medicinal capabilities only slightly less awesome than San Rocco’s, and Veronese’s scene emphasizes the miraculous nature of his power (he spurns the offered box of potions) and the impotence of non-Christian treatment (symbolized by the limbless figure of Asclepius, the classical god of medicine).

Founded in the ninth century and often rebuilt, the church of Sant’Eufemia is one of Venice’s most engaging stylistic discords: late sixteenth-century portico, nave and aisles still ordered out as in the original basilica (with some eleventh-century columns and capitals), stucco work and painted decoration in eighteenth-century boudoir mode. It has one good painting, immediately on your right as you go in: St Roch and an Angel (with lunette of Madonna and Child ), the central panel of a triptych painted in 1480 by Bartolomeo Vivarini .

There’s not much point in going past the Stucky building: Sacca Fisola , the next island along, is all modern apartments, bordered on one side by boatyards and on the other by the site at which waste is mixed with silt to form the basic material of land reclamation in the lagoon.

For a taste of the economic past and present of La Giudecca, double back along the waterfront and then turn down the Fondamenta del Rio di Sant’Eufemia; a circuitous stroll from the run-down Campo di San Cosma (where the church of SS Cosma e Damiano, having undergone a flurry of restoration, has now once again been left to crumble) to the Rio Ponte Lungo will take you through the core of Giudecca’s former manufacturing district. The interior of the island on the other side of the Rio Ponte Lungo is not so densely built up, with a clean amount of open space (even vegetable gardens) around the Redentore and the hulk of Santa Croce church (built c.1510 and long ago deconsecrated). Frustratingly, hardly any of La Giudecca’s alleyways lead down to the lagune on the south side; if you want a view crossways the water in that direction, it’s best to take Calle Michelangelo, which comes onto the main fondamenta between the Zitelle and the youth hostel