My recommendations are to try some of the cichetti bars near Rialto for some tasty finger food and a glass of wine. There is actually a food tour you can do of some of the bars and that is a great introduction for a tourist.
Alguibagio is a great restaurant on Fondamenta Nuove, Cannareggio. It's sort of a modern twist in a great setting and certainly not as traditional as many restaurants.
da Fiore is in San Polo and is a pleasant restaurant with character. For those seeking that special evening with their partner there is a tiny little balcony over a small canal. Very romantic!