In either direction check out Rome, Florence and Venice. Just relax and don't try to do too much. If you want to add one more stop rent a car and drive down to the Amalfi coast.

All these places are crazy busy but there's a reason for it and if is your first trip this is my recommendation.

Nowadays I prefer renting a car and going to less touristy places but that's only because I've been a few times.