A surprisingly nice and prompt train took me from Bologna to Venice. The train station for Venezia (not Venezia Mestre, the mainland industrial area next door) is on the main Venice Island itself, from where you can take a vaporetto (water-bus) down the Grand Canal that cuts through the island. From there, unless you plunk down big $ for a gondolla or water-taxi, it's a completely walking-only city – no cars, yay!
Just a minute's walk away from the hotel I was staying in was the Basilica di Santa Maria Gloriosa dei Frari, which is basically the #2 church on the island, quite nice, and the Scuola Grande di San Rocco, which contains a large number of paintings including some big works by Venice fave Tintoretto. I took the audioguide for the latter and found it disappointing.
I wouldn't say these are must-sees but they're a lot less crowded than the Piazza San Marco sites below and quite nice. You could happily skip the Scuola Grande if you don't want to see it's art specifically; there's plenty of big art in the Palazzo Ducale and the art museum anyway.
The Accademia contains mostly 18th century art from Venice. It was interesting, but nothing in it really struck me. The audioguide was OK but didn't add as much insight as it should. I'd probably skip the Accademia if you have seen other art from this period elsewhere sometime and aren't interested in such art specifically.
After the Grand Canal itself, the main center of attraction on Venice Island is the Piazza San Marco (St Mark's Square), containing both the big Basilica di San Marco church and the Doge's Palace, the Palazzo Ducale.
The Doge was the head of the Venezian state, and although elected for life he was very tightly constrained in power – for example, he couldn't receive ambassadors or delegations alone, all his letters were read by censors, and he couldn't own any foreign property. Still, the position conferred immense prestige and privilege, and the palace is a standing demonstration to this and to the wealth of the Venezian state as a whole. It includes the rooms and giant halls used by the Senate and there's a lot of rooms to see – many featuring big Venezian artworks from the time.
No photos allowed inside unfortunately. The audioguide was worthwhile though very annoying to use – loud bleeps before each artwork, no pause, fast forward, or rewind – so it was frustrating at times. Allow half a day for the palace, including a wander through the jail over the Bridge of Sighs.
After those places I really didn't have much interest in going to the big church on St Mark's square, the Basilica di San Marco, especially as it only opens to tourists at 9:45 these days and there's always a queue well before then. Still, looks pretty from the outside :).
The thing I enjoyed the most on Venice Island was just wandering around taking in the sights. Human traffic around the main tourist channels was pretty slow which could be frustrating, so try and leave lots of time to get places – especially as you'll get lost!
Maps are absolutely essential but they're relatively poor, leaving off some things that are effectively streets, names not matching the signs etc., and you have to really twist and turn to get around the place so it's not always obvious where you are. And GPS does not work most places as you can only see a small slice of sky straight up most of the time.
It's actually loads of fun – at one point I left my friends' travel book at a restaurant accidentally, and had to get back to it… from the other side of town, where I had randomly wandered to without direction. And since I got to the restaurant the same way, I had no idea what its address was (the postal numbers they use in phone listings & receipts are of no use for navigation, they don't correspond to streets directly). Basically it was like geocaching, with no GPS, no idea what the destination was, and instead of finding a cache of someone else's junk, I got my stuff back! It was cool, most fun I'd had so far in Venice :).
I generally enjoyed hanging out in Venice, but the crush in the main tourist areas definitely gets a bit much. And I am now thoroughly sick of gelato after eating two or three a day to keep cool in the humid summer heat! The food was OK but not as good as elsewhere in Italy, which is to be expected for a tourist spot. The canals and buildings are really nice though and it does give the city a unique feel. I really enjoyed getting off the main island though.