Without a doubt our favorite is Trattoria Pizzeria Al Vecio Portal, which is set in a quiet spot (Campiello della Pescheria). There is an interior garden and it is very popular with the locals. House specialities are the fish dishes (Ravioli di Pesce, Spaghetti alle vongole, the tuna..,). You can eat for a good price, about 10-15€ per person.
Placed in a more lively are (though still full of locals) is Al Vecio Calice, located at the beginning of Via Giuseppe Garibaldi and with a pleasant terrace overlooking the sea. If you just want to snack, they have excellent cichetti, bruschetas and focaccias. But if you are hungry, they prepare the typical pasta recipes of Italian cuisine (9-11 €). Excellent tagliolini ai frutti di mare and penne all'arrabiata, although the truth is that all are good. The pizzas are more for tastes (there are those who love them and who hate them :-). The wine glasses will go for 3-5 €.
Another alternative (if the previous one is full) is El Refolo, also on Via Giuseppe Garibaldi (more towards the center, on the other side of where Calle del Forno starts). Their specialty is the high quality sausages, which you can take in rations (tagliere of 10-19 €), or in small sandwiches (paninettos at 2,20 €). Accompany it with a fantastic glass of red wine (€ 3-4) or a Spritz (€ 3).