Much better to take a breather from the crowds and the glamour. Everybody, but everybody, gets lost in Venice. That's part of the charm of the place, and beyond doubt the best way of finding that delightful little campo or waterside locanda that will become all your own. The secret is to be based in the centre, but to make sure that you do your getting lost well away from the madding crowds. In the process, you'll start to discover a Venice where the pace is less hectic, where you can relax and enjoy a holiday from guidebook fatigue.
Within mainland Venice, Dorsoduro fits the bill perfectly. That's the area of the city on the south side of the Grand Canal, across the Accademia Bridge, an enchanting maze of alleys and waterways with its own (less well documented) array of treasures and many of the best restaurants in Venice.
The walk over to Dorsoduro is a pleasure in itself. Leave Piazza San Marco from the western end and, by way of a brief diversion, weave your way across into the charming Campo San Fantin, site of a Renaissance church, the Fenice opera house (currently being rebuilt yet again, following the recent fire) and a friendly open-air restaurant called Al Teatro where you can eat outside in far less cramped conditions than in the restaurants nearer San Marco - and at half the price.
Then head for the Accademia Bridge via Campo Santo Stefano (also known as the Campo Francesco Morosini), a large square that was the site of Venice's last bullfight in 1802 and is home to two superb palazzi, a Gothic church with a famously leaning campanile, and various reasonable eateries - among them Paolin, rightly celebrated for its ice-creams.
Already the crowds will be thinning. Once you cross the bridge into Dorsoduro and are out of immediate range of the Accademia Gallery you will feel that you're in a different city altogether: the quiet, slightly mysterious back-street Venice of countless romantic films.
Ahead, slightly to your left as you cross the bridge is the tree-lined Rio Terra Antonio Foscarini, which runs directly south to the Giudecca Canal and forms a useful natural divide between eastern and western parts of Dorsoduro.
To the east of that divide, the walk along the Grand Canal towards the magnificent Basilica di Santa Maria della Salute will take you past the Palazzo Barbaro, where Robert Browning gave readings, Claude Monet painted and Henry James wrote The Aspern Papers, and to the eccentric Palazzo Venier dei Leoni (eccentric because only one floor was completed), home from 1949 until her death in 1979 of the American art-lover Peggy Guggenheim. The building and her fabulous collection of 20th-century art are open to the public, and are an absolute "must see" of Alternative Venice.
Continue round the tip of this eastern section of Dorsoduro, taking in the magical view across the water to San Marco, and you'll come to Zattere, a quayside overlooking the Giudecca Canal and the sunniest spot in Venice. John Ruskin stayed here towards the end of his life, writing part of The Stones of Venice at the Pensione Calcina. Zattere has a string of waterfront restaurants, all pleasant for outside eating. Try Linea d'Ombra for fish, or Alle Zattere for pizza.
Other recommended eating places in this part of Dorsoduro are the leafy courtyard of the Hotel Agli Alboretti, to your right on Rio Terra Antonio Foscarini as you walk back from Zattere in the direction of the Accademia Bridge, and (just off to your right before you reach the bridge) the Al Cugnai restaurant, on Piscina del Forner.
The western section of Dorsoduro is slightly wider and more spacious, the perfect locality for soaking up street-market life. In Campo Santa Barbara are book-binders and furniture restorers, and as you leave the square you'll be hit by a blaze of colour from the fruit and vegetable boats moored by the flat-topped Ponte dei Pugni.
The narrow Rio Terra Canal street, with its fascinating mask shops, leads you to the lovely Campo di Santa Margherita - a long rectangle bustling with local bars and restaurants, where your soaking up of the atmosphere can become rather more literal.
A final suggestion for avoiding the tourist rat-run during a stay in Venice: if time allows you only one day to make the statutory boat trip to an island, ignore Murano, where you'll get mugged by glass-blowers trying to lure you into awful factories, and avoid Torcello, where you'll get mugged by Harold Pinter fans quoting morosely from Betrayal and then telling you how cheap it is at the island's Locanda Cipriani restaurant. Instead, take off on a ferry for Burano (Line 14 from near San Marco takes one hour 20 minutes; Line 12 from Fondamente Nuove takes 50 minutes).
Burano is a delight. In one way it's a less lavish miniature of Venice, with its own system of canals, bridges, alleyways and so on, yet, by comparison, it is quite charmingly homely and devoid of the ornamentation that can sometimes become almost overpowering in the city. In another way, with its brightly painted houses and its local population of lace-makers and fishermen, it resembles nothing so much as a little Greek island - with the unassailable advantage of serving Italian food.
Most of the restaurants are on Via Baldassure Galuppi (named after the composer, Burano's most famous son). Most expensive among them is the highly rated Trattoria da Romano, a former favourite of artists and latter- day haunt, so I'm told, of Michael Winner. All of the restaurants are better value than at San Marco or the Rialto.
But for the opposite end of the price range, trot across the footbridge linking Burano to the even tinier island of Mazzorbo and seek out its sole trattoria, Alla Maddalena (beside the landing stage). Cheap, freshly cooked local food in simple surroundings, and not a restaurant critic in sight...
Ryanair (0541 569 569) offers return fares from Stansted to Treviso airport (about 19 miles from Venice) starting at pounds 129.20 (including taxes). Travellers must spend two nights or a Saturday night to qualify for the lower fares. For flights to Venice's Marco Polo airport, Italy Sky Shuttle (0181-748 1333) offers return fares from Gatwick starting at pounds 150 (including taxes)