Just back from Venice, and thought I'd post this note especially apropos to the just-posted query.
First, what to avoid: most restaurants near San Marco. There are lots of visible red flags - only tourists eating there (and since many have outdoor tables along the sidewalk you can see exactly what the food looks like), the menus are posted on poster-size placards in several languages, and bored waiters try to attract passers-by to sit down.
Within Piazza San Marco, spending some time at one of the outdoor cafes - Florian or Quadri - is a must. They are overpriced but wonderful, especially in the evening when the orchestras are playing and a cool breeze is in the air.
The restaurants we enjoyed the most were Corte Sconta (Calle del Pestrin, just off the Riva degli Schiavoni, just before the Arsenale vaporetto stop) and Acqua Pazza (in Campo San Angelo). Corte Sconta has surely already been covered on this board, but I can report few tourists, gracious service, exemplary food, and high but fair prices. We started with the seafood antipasti, which consisted of 7 different small dishes. They included spider crab, a salmon pate, swordfish carpaccio, clams in a garlic/ginger marinade (fabulous!), and a few things I guess I cannot remember. We both had the delicious black pasta with seafood, then shared (even though we were totally full) tiny deep-fried soft-shell crabs (super tasty and fresh).
Acqua Pazza is a newish quite stylish restaurant specializing in seafood and neopolitan style pizza. We went there for lunch and had pizzas, which were as good as any we've had in NY. My husband had the pizza with mixed seafood, which had a very generous serving of high-quality seafood. Mine had arugula and speck wit high quality mozarella. We saw large, beautiful platters of seafood being carried out of the kitchen but did not have time to return to try this part of the menu. My only gripe about this place was that it seemed a bit overpriced; I was also unhappy about the 4 Euro per person cover charge, which basically covered nothing since they did not serve us bread.
We also ate at Ristorante da Raffaele (at Ponte delle Ostreghe, roughly halfway between the Accademia and San Marco). The food here was good but not great, and I especially enjoyed a special of very fresh orata. It is a pleasant place to sit, along a small canal.
For a simple and inexpensive lunch near Santa Zaccaria, try Trattoria Al Greci at Fondamenta San Lorenzo. Inepxensive pastas and pizzas, also along a pretty canal.
Less satisfactory was Locanda Antica Montin (or something like that - it is written up in many tourist guides), where I had had a great meal a few years before. The food was also good but nothing special, but maybe we just ordered the wrong things. They have a lovely enclosed garden.
There is an abundance of restaurants in Venice but this is a city where you definitely want to do research to avoid disappointment. Next time I'd like to try a few other restaurants recommended to me by friends I trust: Osteria da Fiore, Alle Testiere, and Al Gondolieri.