What, You Only Have a Day
Borghese museum is a must see and the park there is nice.
Palazzo Altemps directly north of P.za Navona has a great sculpture collection.
I like Galleria Doria Pamphili because the paintings are all just hanging there to be regarded without tags (you can get a book with details).
The Pantheon is near p.za Navona and is spectacular.
S.ta Maria in Prassede is a quiet jewel with byzantine mosaics
San Clemente on via Labicana just down the street from the coloseum is 3 levels of history in one place and I think is really worthwhile. If you were to do S.ta Maria Maggiore, S.ta Prassede, S. Clemente and S. Giovanni it wouldn't take that long and would be a good variety.
Trastevere seems to be popular with everyone (just grab the 8 trolley at largo Argentina). It's too touristy for me, but is actually full of shopping/dining/little site kind of places. S.ta Maria in Trastevere is a beautiful piazza and church worth a trip.
See Travelogue "Hit the Highlights" for a serious walk about town.