The first thing to know about Venice is that it's smaller than you (probably) expect. You also don't actually need to take boats everywhere (which may not be a revelation to some, but it surprised me!) - you can get almost anywhere on foot. But the fact that the streets are constantly intersected by canals and bridges makes them incredibly labyrinthine; I got lost in Venice more frequently than anywhere else I've been. Until I admitted defeat and switched on Google Maps, I kept wandering around in circles trying to find places I wanted to go, only to discover I'd ended up somewhere I thought was in the opposite direction. So my main recommendation is: make sure you've done whatever you need to do with your phone to use mobile internet... or else take a very detailed map with you.
As for what I saw and did, it's worth noting that many of the most famous sights of Venice are exactly that - sights; you don't necessarily have to pay to go inside places in order to experience the best view of them. (For example, the image of Santa Maria della Salute seen from the Ponte dell'Accademia is iconic, but the church is underwhelming inside.) I found that wandering the whole city was the best way to see it. The best-known areas - anywhere around St Mark's Square and the main two bridges - are constantly full of people, but further afield it can be so quiet and calm (and just as beautiful) that it feels like you're worlds away from the crowds. In particular, I really enjoyed walking around the districts of Cannaregio and Castello.
I'm so glad to have seen Venice, and I'd really recommend it for a short holiday, or a daytrip if you're visiting elsewhere in Italy. You can easily see the whole city in less than a week; if you didn't want to go beyond the main tourist areas, you could probably see all of the major attractions in a day. It's so picturesque that you're guaranteed breathtaking views wherever you go.
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