It's been several years since I was there, but the Vatican Museum is an absolute must-see, Montyracing2 - reserve at least a half-day for strolling around the place, and bask in the opulence and hypocrisy of the Universal Church.
You could also fit in St Peter Basilica/Square and Castello Sant Angello on the same day.
From Castello Sant Angello, you can walk down the side of the Tevere as far as the Palatino. If you climb up the Palatino, you get a great view overlooking the Forum, with the Colliseum in the background. Both the Forum and the Colloseum also be done in the same shift too, with the latter having a particularly good audio-tour as I recall. The Pantheon is also very much worth a look, though will only take you 15 minutes to have a nose around.
Make sure you have a gellato by the Trevi fountain, a coffee on Piazza Novona, and don't forget to wash your hands for luck in the fountain at the foot of the Spanish Steps.
Rome is reasonably compact for a major European city, and I'd recommend walking everywhere if you can (rather than taking the Metro), because you will miss something worthwhile otherwise.
As for eats, you can't really go wrong anywhere in Italy, but Mrs Grass and myself had a great scoff at a place called 'Il Due Collone'. It's on the Via Del Seminario, not far from the Pantheon, and is highly recommended.
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