to be honest, so much of modern Rome is built over ancient Rome that there's not as much left as you might expect. The Colosseum and the Forum are the main survivors, and the main museum is good. There's a lot more of Rome of the Popes surviving from the Middle Ages and Renaissance - especially St Peter's, which is well worth a visit. If you want to get some feeling of what a whole Roman town is like, visit Pompeii (near Naples) or other deserted cities abroad such as Leptis Magna in Libya (there are good remains in Tunisia and Morocco too, and other colosseums in Tunisia, Croatia etc... the Romans really got around).
Sorry - I know you'll just be doing Rome this time round, but you might like to bear them in mind for the future.