Here is a list of different restaurants in terms of range and places. Amonsgt the venetian dishes give a try to Baccala, pasta alla Vongole & shrimp saour, capelunghe (depending on the season) :

Il Paradiso Perduto  roots-vintage-canteen, always animated spot. Amazing for aperitivo, lunch, dinner, or party (there is a piano on stage and the owner like to party).

Hotel Monaco Gran Canal (in San Marco) has a beautiful (expensive) restaurant, in summer prefer a table outside on the terrace over the grand canal.

La Calcina. (on Zattere/Dorsoduro). Wonderful Terrace, perfect for sunny lunch or any sunny day.

Antiche carampane (#1 for fish)(in San Polo). Away from tourists secret spot being the Rialto.

Alle Testiere (incredible small restaurant near Campo Santa Maria Formosa / need a reservation).

A Beccafico, wonderful sicilian restaurant in the middle of Campo San Stefano. Amazing food, funny waiters. Terrace during the summer.

- La Mascareta, amazing restaurant held by italian figure Maura Lorenzon. Just above Campo santa Maria Formosa. Expect good wine tasting.

- Il Refolo (Santa Croce 1459 // Campo San Giacomo de l'orio +390415240016). Amazing terrace during the summer.

Al Giardinetto, (Castello) (very nice inner garden, a classic a people "who know").

- Basara sushi, (San Marco) best Milanese sushi in town. A few meters away from San Marco square.

Vecia Cavana, (Cannaregio). Between Ca d'Oro and Fondamenta Nuove (Campo dei Apostoli), this big restaurant serve a delicate cuisine.

Palazzina G, (San Marco), inside only I would suggest only fr romantic dinner. Located in a beautiful hype hotel decorated by Philippe Starck. (perfect in winter)

Trattoria Ai Cacciatori, (Giudecca). Simple to find, little terrace for summer lunch or diner. Best food so far in Giudecca island.

Al Remer (Rialto)(major interest is the spot for the view, just in front of Rialto on a charming little campo)

Harry's bar (in San Marco) a gold for winter. (try lemon pie)

Ancorra (Rialto mercato) (Aperitivo & restaurant). perfect to start an aperitivo & eat in the terrace outside during summer.

- Trattoria Al Diporto (santa Elena), this is a typically venetian place best know for his 'frittura mister'.