In the three years I lived in Rome, I took the train almost every weekend to Venice, but only during late autumn and winter. This is the time when tourism is down significantly, and a time when the locals reclaim the city. Venice as it truly is is best experienced during this period. Late March is fine, but tourism starts picking up at this time, and you may glimpse what the city must be like in late spring and summer.
I second the suggestion above regarding Alle Testiere. A great restaurant serving fish and seafood only. One wonders how it is possible for the chef to turn out such wonderful food working in a kitchen the size of a closet. Do not be surprised if you find some dishes lightly seasoned with ginger and cinnamon, flavors not normally associated with Italy. The waiter will remind you, however, that Venice once was a great seafaring power, and brought back spices from the East that were gradually incorporated into the local cuisine.
It used to be that Enoteca Ai Artisti was one of the best kept secrets among those who knew Venice, and certainly by the people who lived in the Dorsoduro section of Venice, which is where the Enoteca is located. I hear it has been discovered, and now there are throngs of people who fill the place day and night. However, you may want to venture there anyway since the Peggy Guggenheim Museum and the Galleria dell’Accademia are both located in the Dorsoduro. The Enoteca Ai Artisti serves honest cooking executed with real skill by the chef. And as the name indicates, it is a place to drink wine by the glass or by the bottle. The selection is admirable.
Also in the Dorsoduro, is the estimable Cantinone Gia Schiavi. It is a wine bar that serves a good selection of cichetti (think tapas). It is a convivial place, popular with the locals. During the evenings, even in late autumn, the crowd spills out onto the canal. Here the wine flows freely, the delicious cichetti consumed in great quantities, and the conversation so animated that one can only return time and again. The Cantinone also doubles as a wine shop, and here you will find a dizzying selection.
Venice remains one of the great beauties in the world, owing in part, paradoxically, to its decay. Wake up early, and go to the Piazza San Marco when the sun is beginning its ascent. Go when the only denizens are the pigeons and perhaps an old fellow sweeping the square. Stand in the middle of the piazza and you will be struck at how magnificently beautiful this place is. It will take your breath away. And if you should ever be so lucky, you will stand here when a light snow is falling. You will be haunted by this memory for all time.