Steven,
I'd also vote for 3 nights, but at least 2 before you head elsewhere. We were just in Venice in early October, and we were there for just one night. We took a shared water taxi from the airport (which my husband calls a must-do, as the experience itself was great fun), then we went to mass at St.Marks (while it was all lighted inside...which makes a huge difference in the beauty), then toured the museum/balcony/saw the bronze horses upstairs). We also took the advice in the RS guidebook and took the varparetto up the Grand Canal, waiting for one where we could get seats in front of the wheelhouse. That was great fun, and we actually did a loop. Fun talking to locals who were on the same vaparetto, heading home from work, etc. Then quick dinner and early to bed.
We walked by the wonderful restaurants that are recommended in the RS guidebook, one was closed on Sunday night, and the another was booked up. Other interesting ones did not open until 7:30 or 8pm, and we were feeling the effects of the time zone changes, so we had a light dinner and were in bed early.
The next a.m. we visited Doge's Palace (where we were actually offered a senior discount), then we meandered around the shops on St. Mark's Square, etc. and then it was time to head toward our small ship for boarding.
We arrived on a Sunday and left on a Monday. There were things we would have LOVED to do, but time did not permit. We would have loved to climb one of the bell towers, and we would have loved to go to one or two of the islands.
The hordes of people probably would vary based on WHEN you are going. I don't think I spotted your WHEN. Other than right at the waterfront in front of the large hotels, I was surprised it was not more crowded. St. Marks Square was brisk but not hordes, and we had maybe a 15-minute wait to get in Doge's Palace (no reservations/no advance tickets...arrived around 10am). We may have just been lucky.
Our hotel was the Hotel Le Isole, which is an easy (no more than 5-minute) walk from the vaparetto stops off the Grand Canal, and about that much time (or less) to the heart of St. Mark's Square. It was an extremely quiet location,convenient, but in some ways it seemed like miles away (lack of crowds). We would absolutely stay there again. Price, location, cleanliness, great breakfast, very kind staff. The only thing we had wished for was a larger bathroom...ours was rather tiny, but it worked. We had a balcony overlooking one of the small canals, as well as a large window (that opened) overlooking the other approach on the same canal, and my husband had great fun watching the gondoliers prep for the day, as well as watching the equivalent of the UPS delivery boat, and the laundry boat make their stops.
I'd heard some people say they would not give Venice more than a day, but we left wanting for more. Our ship actually returned to Venice, so it was lovely seeing Venice again in the very early morning as we sailed into port.
Enjoy your trip.