Hordes of tourists and high prices put many people off Venice, but you don’t have to venture far from San Marco to find quiet streets, locals’ haunts and bargains. Dorsoduro, a hop over the Grand Canal via the Accademia bridge, has as many great museums, galleries and churches, but a fraction of the crowds and costs. Artists and designers are moving into the eastern end of the sestiere, and the north-western tip has the city’s liveliest nightlife, in the alleyways around a large studenty square.

1. Start at the Gallerie dell’Accademia (€15), which has an enormous collection of artworks by the Venetian greats – Titian, Veronese, Tintoretto, Tiepolo. The Accademia’s 20-plus rooms can be a little overwhelming, so make sure you don’t miss Giorgione’s heartbreaking Old Woman in room four. The gallery opens at 8.15am – get there early to beat the crowds.

2. Head down Calle Sant’Agnese (which turns into Piscina Forner) for some souvenir shopping: a cluster of shops sell tasteful items at reasonable prices with no hard sell. You might pick up simple Murano glass earrings for €12, or traditional silk slippers, or a carnevale mask. Further on are small, modern galleries, including Venice Projects and Bac Art. Stop for a coffee at the misleadingly named Corner Pub at 684 Calle della Chiesa, a hole-in-the-wall bar/cafe with a few stools outside – there’s no signage, so keep your eyes peeled.

3. The Peggy Guggenheim Collection (€14) is Venice’s major modern art gallery, with a piece or two by most 20th-centuries masters; Jackson Pollock gets a whole room. Marino Marini’s Angel of the Citadel will make you smile (it’s a man on a horse with arms widespread and a huge erection), and is on a lovely terrace backing on to the Grand Canal. The Guggenheim also has great temporary exhibitions – the current one, For Your Eyes Only (until 31 August), is a brilliant private collection spanning mannerism to surrealism.

4. Dorsoduro has lots of atmospheric bacari, bars that serve cheap ciccheti (small snacks) all day, so a bacaro crawl is a great option for lunch. The best in the area is Cantina del Vino Già Schiavi (992 Fondamenta Nani), aka Cantinone or Al Bottegon, a wine shop-cum-bar. Crostini are topped with salt cod and wild garlic, pistachio cream or alioli with flower petals; local customers include dapper older gentlemen and jovial police officers. A few doors along is Osteria al Squero, which is even cheaper: crostini are €1 and wine is from €1.20 a glass. At both spots you can eat outside by the canal; the latter is opposite the city’s oldest working gondola yard, the 17th-century Squero di San Trovaso. It’s one of just two surviving squeri in Venice – look out for Lorenzo, the master boatbuilder, hard at work.

5. You can’t go to Venice without visiting at least one palazzo museum, and Ca’ Rezzonico (€8) is much more manageable than the more famous Palazzo Ducale or Museo Correr in San Marco. The splendid marble-fronted building houses the city’s 18th-century artefacts, including paintings and frescoes by Tiepolo, antique furniture and Venetian glass.

6. You are similarly spoiled for choice when it comes to churches, but Dorsoduro has a real gem: San Sebastiano, the parish church of Veronese. His paintings adorn the sacristy and nave ceilings, the walls, the organ shutters and around the altar. Being tucked away at the western end of Dorsoduro, it attracts far fewer visitors than, say, San Rocco in San Polo, which is famed for its Tintorettos.

7. After all that culture, it must be time for an ice-cream. Gelateria Nico opened in 1937 and is still serving its speciality, praline with cream. Eat it as you stroll along the Fondamenta Zattere, the waterfront on the Canale della Giudecca (separating Dorsoduro from Giudecca island). You can stop for a prosecco at Laguna, next to the vaporetto stop. It’s not the cheapest spot – prosecco is €4 – but it’s a great place for people-watching, as is Al Chioschetto, a little pavement kiosk that often has a live band, and whose outdoor tables are always packed with people drinking the ubiquitous orange spritz aperitifs. From Zattere you can take a free shuttle boat to the Hilton Molino Stucky which has a rooftop bar and was converted from a huge flour mill.

8. For dinner, try Calle Lunga San Barnaba, a cobbled street full of restaurants. Al Profeta, on the left at its eastern end, serves fantastic meat dishes – deep-fried, mince-stuffed olives, giant ravioli with sweetbreads, duck ragù, venison with porcini (main courses around €13, litre of house wine €10) – in a big courtyard garden.

9. If you have the energy for late-night drinks, try Campo Santa Margherita, usually busy with students. Tiny Ai Do Draghi is one of the best bars, playing great music from blues to Bowie (rather than pumping beats), with good prosecco for €2.50. All the bars serve spritz for about €2 – made with Campari, Aperol, Select or Cynar. Al Bocon Divino is very friendly – if you admire a local’s dog, be prepared for it to be plonked on your lap – and serves a lethal negroni cocktail. After one of those, it’s probably time to call it a night …

10. Rocky Casale, guidebook writer and author

Book a cooking class at the Enrica Rocca Cooking School (half day from €160, including full dinner). It’s a great way to dovetail seeing the neighbourhood and having a great lunch or dinner. Her cooking reintroduces the spices that Venice was famous for in the times of the republic (until 1797).

11. Where to stay

There is no getting away from it – accommodation in Venice is expensive. There are a couple of monasteries with guest rooms in Dorsoduro (Don Orione Artigianelli, Le Romite), but even there, doubles start at more than €100. The only way to get a relative bargain is to book well in advance; at least six months.

Hotels tend towards chintzy, but one exception is Ca’ Pisani, a 14th-century palazzo restored in art deco meets steampunk style, with original 1930s touches (including a fantastic early rowing machine). Breakfast is particularly good – it was recently overhauled by a “breakfast expert”– and the location is ideal, between the Accademia and the Zattere.

A melancholy old violin player busks near the hotel every day – “same time, same place, same three notes”, said a local – which gives your stay a haunting soundtrack.

• +39 041.2401411, capisanihotel.it. Doubles from €124 B&B