Other Rome stuff not usually mentioned:
Museum of the Risorgimento (Reunification) in the attic of the Victor Emanuel monument - great collection of WWI battle art.
St. Clement's church (Santo Clemente?) - ground level regular church, one level down medieval church, two levels down, ruin of pagan church
Capitoline Hill ruins is a great walk on a nice day
Spanish Steps, go up turn left walk along ridge through nice residential area with great view of Rome, pass statue of guy waving pistol, forget his deal but he's pissed, arrive at park with views, drop down hill to Piazza del Popolo, where there's two identical churches side by side.

Other sites if you're going past:
Ferrari museum in Maranello
Leonardo stuff in Vinci (not a lot but a nice break if you're nearby)