My first piece of advice about dining in Venice is to steer clear of places surrounding St. Mark's Square.  I don't find the atmosphere to be overly friendly or the food to be anything special.

One of my favorite places to enjoy eating are at any of the famous Venetian cicchetti spots.  What is cicchetti?  It's a kind of Venetian tapas.  Walk in, point to what you like, get a glass of wine or light cocktail, sit around with the social crowd and enjoy.  For less than 5 euros, an enjoyable light lunch or snack, Venetian-style, is to be had.

Osteria Al Squero:  Located in the Dorsudoro section, this spot is always busy.  What makes it so enjoyable is that it sits on a canal across from where craftsmen make the wooden gondolas.  It's a great spot to pick up a spritz (usually white wine or prosecco with Aperol), or a wine and snack on the various delights served on a small piece of bread.  I like to sit on the edge of the canal and chat with other travelers.

Another wonderful cicchetti bar, just down the canal is Cantine del Vino gia Schiavi.  I think the wines and food is a bit better than Osteria Al Squero and still the prices are low.   In fact, bring in your own liter bottle, they will fill it with wine for 4 euro.

For a sit down dinner,  Ristorante Cantinone Storico is in between the Accademia and the Peggy Guggenheim Collection, again in the Dorsudoro section.  Dine comfortably indoors or on the terrace on the quiet canal, away from the big crowds. We find the staff to be friendly and helpful.  The caprese salad is especially fresh.  Tuna with olive oil is light and tasty.  They have plenty of non-fish pasta dishes but fish is the feature here.