My DH is Venetian... Here are some suggestions that he has put together for people who ask him for recommendations:
Eat "chicchetti" (Venetian tapas) recommended "tris di baccala" and more, don't forget to have a glass of "vino bianco"... and try the spritz! Venice is home of the Aperol Spritz and if you stay away from the main areas it's not that expensive.
"Cantina Do Spade" (near Rialto Bridge)
cantinadospade.it?
"Cantine del Vino Già Schiavi"
Fondamenta Nani, 992
Across from the one above there is the "Squero di San Trovaso" the place where Gondolas are built and repaired ;-) and it is just round the corner from there are the famous Zattere where you will be able to appreciate the most beautiful sunsets of Venice.
Even more there is a gelateria Nico where you can get "Il Gianduiotto": A solid block of hazelnut icecream drowned in a glass jam-packed with a lot of fresh whipped cream!
If you want to visit the birthplace of the bellini cocktail go to Harry's Bar (may cost you a bit).
HARRY'S BAR
Calle Vallaresso, 1323
Good restaurants where the Venetians go:
"Al nono risorto"
Sotoportego De Siora Bettina
Santa Croce, 2338,
"Vecio Fritolin Restaurant"
Calle della Regina, 2262,
30135 Sestiere Santa Croce,
www.veciofritolin.it/
"ai quattro ferri"
Sestiere Dorsoduro,
30123 Venice,
"la zucca"
Santa Croce, 1762
TO SEE
Peggy Guggenheim Collection (Museum)
Palazzo ducale (Doge's Palace, Venice)
Santa Maria Gloriosa dei Frari, Church (Basilica) usually just called the Frari, is one of the greatest churches in the city. Go inside to see the paintings.
The Gallerie dell'Accademia is a museum gallery of pre-19th century art.
Half day excursion to Murano, Burano and Torcello, these are the little islands.
www.venetoinside.com/en/tours_in_veneto/venice_tours/regular_tours_in_venice/half_day_excursion_to_murano_burano_and_torcello/
Hope that helps!