I read this in one of my guidebooks before I went: "The best thing to do in Venice is get lost in Venice." Seemed like a ridiculous plan, but it turns out to be true. I've been twice now, and both times I intentionally wandered by myself. Once slowly and with my camera, the other in the early morning and in my running shoes. Both times I saw (and smelled) things I otherwise wouldn't have on the beaten down tourist piazzas and streets/canals. Venice is a maze of intrigue and history, and getting lost is worth it. It's a tiny island and you always hit the main path at some point.