Day 1 - Trevi Fountain, Spanish steps, Piazza Navona, Ignazio di Loyola, Pantheon, and everything in between.
Day 2 - Vatican Museum, St. Paul's, Castel San't Angelo
Day 3 - Coloseo, the Forum, Palatino Hill, and Capitoline Museum
Day 4 - San Clemente (super cool and underated), San Giovanni en Laterano, then up to the neighborhood around Piazza della Republica, then Piazza del Popolo, then strolled through everything we saw on Day 1, and spent the evening in Trastevere
Day 5 - Took the train to Venice
Day 6 - explored Venice

We loved it. I think spending anything less than 3 full days in Rome would be a mistake. You'd miss too much.