chiming in here; I lived there for a year and know the city pretty well. It’s absolutely worth visiting, and while tourism is the primary industry, there are also two universities in town, so tourism is not the only industry. Wheeled vehicles are not allowed anywhere in the historic city center, so it’s a nice relaxing break from dodging scooters in other Italian cities… if you wander away from the main streets, it’s just blissful silence and the sound of lapping water.
I definitely think you should go for at least 3 days. One of those days should be devoted to getting gloriously lost somewhere off the beaten path (buy a good map, the kind that shows ALL the streets)–there are no bad neighborhoods to wander into in Venice, just quiet and beautifully preserved streets. This is my #1 suggestion for what to do in Venice. However, understand that the street numbering system is completely random, and there are no taxis, so make absolutely sure you get a business card from your hotel that shows the location (it will give directions on how to navigate from the nearest landmark) and plan on having to walk back to your hotel, not throwing in the towel and picking up a cab.
(Well, that’s not quite true–there are incredibly expensive water taxis, but they don’t just cruise around back alleys waiting to pick people up.)
One day should be devoted to tourist destinations: the Doge’s Palace, St. Mark’s, Santa Maria della Salute, the Accademia, the Guggenheim, the market at the Rialto, etc.
For the third day, I suggest either another day of wandering or a trip out to the outlying islands. Murano is OK (the old churches and glass museum are nice, and of course you’ll be into the glassblowing/beads) but I think Burano is way more fun (colorful houses, traditional lacemakers) and adjacent Torcello is kind of wild and overgrown, interesting for being the oldest settlement in the Venetian lagoon. Or you could go to the Lido, where all the movie stars play.
Do not get a room overlooking a canal. It may seem romantic but canals are smelly. Also, stay away from the main drag near the train station–it’s convenient, but loud and overpriced.
I used to recommend the Hotel Alex to people; it was pretty reasonably priced and in a nice central location. I haven’t been back in a few years but it looks like the current rate is 60-112 Euros for a double room with private bath, 35 to 54 for a single room without a bathroom (i.e. there’s a shared bathroom in the hall) http://www.hotelalexinvenice.com/EN/index.htm
Take a traghetto (gondola ferry that crosses the Grand Canal, costs about a dollar) if you want the gondola experience without having to pay $50 for 1/2 hr or whatever the going rate is.
Verona is a nice city, too, but I think there’s less to see there than in Venice, and it’s less unique. I went to Juliet’s house and saw an opera. I do remember that the HI hostel there is really fantastic–it’s in a 16th-century palazzo with frescoes on the walls, and a garden outside.
Also, if you’re going to the Genova area at the end of your trip, you should absolutely go to Cinque Terre. along with Venice and the Amalfi Coast, one of the best places in Italy to visit.