Venice is the perfect city to get lost in - as long as you've got a map once you want to be "found"!
On our third day, we split into couples (my boyfriend and I, our two friends) and set a meeting point at a certain time. After that, we just walked, with no particular destination in mind. There are so many historical sights in Venice that while picking one or two is a good idea (San Marco, the Bridge of Sighs), trying to plan anything more is almost senseless.
We walked past dozens of churches, beautiful bridges, homes with flowers spilling out of their windows, and places where the rare remaining native Venetians went about daily life. It was lovely, wandering from one surprise to the next and never quite knowing what we'd come across.
The downside is that if you're only in Venice for a few days, you soon realize that you'd need two or three weeks - at least! - to do the city justice. Of course, the upside is that without any plans, and forgetting about your map, you're all the more likely to see sights you might otherwise have ignored.