Venice, Rome, Florance, and Pisa are MUSTS
Venice is really different and just know you are going to get lost, it's ok you'll have more fun that way...it was the richest country at one point so there is a LOT of gold in the palace. Make sure to take the "secret passageway tour" of the palace, it is only a few euros more and well worth it!
Rome is historic and an amazing sight, it is really neat to see ruins right next to new buildings and just wandering around the city and randomly bumping into the Colosseum...a really fun city with good food and lots to see. You must see the Vatican while you are in Rome as well...museum AND church and go to the Coppola to get the amazing view of the Vatican.
Florence is really beautiful, good history there as well...obviously you have to see the Church, Dante's house and church and the Academia Museum (the David is there)
Pisa is a lot of fun to see and walk up and take pictures but you really only need 2-3 hours MAX there...train in, bus to tower (lina rosa - red line in italian but i probably spelled it wrong, go up, take pics, head out!
*for the BEST advice listen to this guy:
http://www.ricksteves.com/