Stay away from San Marco Square!
As a Venetian veteran, I can say that this is one of the prettiest and ugliest cities I've ever visited. Or maybe I should say that the enormous stream of tourists is ugly, throwing shade on the beauties of Venice itself. There's only one thing I can say to people who visit Venice for the first time: stay as far as possible from San Marco Square. You'll find the real beauty in places where less people are.
Insider Tip:Roam around in Castello and Dorsoduro, visit Giardini, visit the Biennale (especially the free exhibitions are amazing, you'll find them all across the city!), the islands, buy a vaporetto 3-day card, Google cheap places to eat, find a bar with locals to drink coffee, try the traghetto gondolas and, if you happen to stumble upon a boat with a few Venetians on it, try to get a lift;)