Spend two days in Venice. It's enough to see just about everything, and not get tired of the winding streets and canals. It's as good a place to go by yourself as it is romantic. Frankly, I didn't find it too romantic. There's too many people. And sitting on the Gondola while the crowds wave at you from the bridge above is hardly a fantasy. Don't expect a lot of activities. It's a lazy city. If you like walking, just walk without expecting anything exceptional. It will be exceptional, I promise.
Insider Tip:Four stops away on the water bus is the happiest, most colourful, most feel good place on the Earth - Burano. If you go to Venice, you have to go to Burano. Just have to.