Been to Italy twice. Both times have been in the northern part. Never been south of Rome. Recommendations for what to see and do.
Venice- Sounds like your heart is set on Venice. I know people love it, but I've been there twice and both times I haven't loved it. Don't make your trip based around your stay there though as it's very far northeast from the rest of the country.
Cinque Terre- You might not have heard of it, but you've certainly seen the pictures of these 5 tiny towns. It's incredible. The views, the hikes between the cities, and the food are amazing. I'd recommend to anyone that this is a must see.
Florence- I've been twice, but both times never a full day. It's a great city and a good area to make your home base if you want to stay centrally located and drive to nearby cities.
Pisa- Only go if you are bored. Worth seeing the Leaning Tower, but that's it. Make it a trip to see for an hour and go somewhere else for the rest of the day.
Siena- It's a cool city, but I got bored after half a day.
I stayed a couple hours south of Florence in the middle of nowhere. It was a resort with a warm spring below so the pools were heated. I'd stay there again in a heartbeat. Great location to everything including small towns nearby, wineries, and amazing view from the hotel. This was the view in the morning from the hotel.