Agree with those who say Venice is made just for wandering for the sake of it. A stunningly beautiful place full of secret corners and nooks and crannies you could probably not find if you set out to look for them, but stumble across as a complete surprise.
And definitely go in St Mark’s, if only to see the original horse bronzes - one of the most beautiful set of statues I have ever seen, and with a great story behind them. You can climb out onto the roof of the cathedral too, and just sit and watch St Mark Square from above, although if you want an even loftier viewpoint for that you can go up the Campanile and see for miles, all the way out to the other islands.
The Doge’s Palace can be done several ways. If you want a whistle stop tour and someone to explain it all for you, then go ahead with the tour. If you want to stop and read the very extensive history of Venice as told through the story of the Doges, then you will need to be in there without a tour. I don’t know, some people like just following a shouting person with a pompom on a stick, I am not one of those people. The underpalace here is essential, don’t just take the short route, head deep down and see the prisoner’s graffiti, very evocative. You see the Bridge of Sighs from the inside here. Also make sure you duck through the unassuming looking archway to see the original famous fresco painting of St Christopher by Titian.
Give Florian’s a swerve unless you like being ripped off, likewise don’t drink anywhere in St Mark’s Square where a reasonably priced coffee will suddenly have so many extras added to it (charge for listening to the house string quartet? Didn’t you know that was extra?) you will wonder if you did in fact have a 3 course dinner instead and just didn’t notice it.
For boats, get the vaporetto along the Grand Canal. Pennies, and worth every one. Gondolas are pricey wherever you get one from, but if you do one cheesy tourist trap thing in Venice it should be this.
Eat on the back streets, not the Grand Canal - you pay extra for the address there. There are lots of lovely small squares and side streets with delicious food served, still atmospheric.
Venice is fab, just don’t waste your time there by filling it with tours and organised excursions - just wander, and find treasure!