Rome is awesome. You could spend lots of time there. Like others, spend more time, less places. You will be happier in the end.
The other advice is to make sure you go off the beaten path. See the locals side of life, not just the touristy places.
Also, if you have time, visit some smaller towns outside of the big places. Since you have a rail pass and a flexible schedule, just get off at a place that strikes your fancy. Gives you a new perspecitve on the people and places. Plus, adds a little adventure to your trip.