The Sistine Chapel. Carbonara. The Trevy Fountain. The Pantheon (go inside). The Temple and the Visitor's Center.
Take a day trip to Florance. Day trip to Pompeii.
Plenty to do.
When I went to Rome, I took a day tour that was awesome. Then spent a day doing whatever I wanted (which included going INTO the incredible Pantheon). Then we went on a 7-day cruise around the Mediterranean, which was awesome.
There's so much to do.