In reply to maybe_si:
Take earplugs! Rome is an incredibly noisy city and never really shuts down. A lot of the major sites are in fairly easy walking distance of the city centre, but getting the Metrebus Carta BIT gives you 3 days on the metro and buses for 16.50 Euros. If you use the metro or bus, ensure you and the Missus have your bags in front of you at all times, never sling a rucksack on your back or a handbag over your shoulder; distraction robbery is popular!
There are a lot of hotels around Termini, these tend to be on the budget side and it's a fairly noisy area (though as above, most of Rome is pretty noisy!). Staying away from the Termini area unless budgetary constraints don't allow would be my advice.
'Must do' things in Rome depends really on your interests. The Forum and Colosseum I'd put on the list, but the Forum can be a bit confusing. St Peter's and the Vatican Museums'll take the good part of a day but the museum is mind-blowing, and the restored Sistine Chapel awesome. Others have mentioned the Pantheon, which is my favourite building in the world, it is stunning, especially if the sun's shining through the oculus (hole), or if it's raining. The roof is 2000 year old poured concrete, the columns at the front were quarried in Egypt, and Raphael is buried there.
But if you 'do' the Pantheon, there are a couple of other things in the area - San Luigi dei Francesi (church of St Louis of France) just to the west contains 3 Caravaggios, and you can just pop in there and gawp at them, and Santa Maria sopra Minerva just south of the Pantheon has a gorgeous little Bernini elephant outside, and the beautiful simple tomb of Fra Angelico inside. There's also the Piazza Navona just to the west of the Pantheon which has super fountains in it, and some nice restaurants. Finally, just north of the Pantheon is Della Parma's Gelateria which in exhaustive tests carried out by a group of post-doctoral students in the early 90s won the title of 'best Gelateria in Rome'. Obviously things may have changed in the last 20 years, but you can compare it with the more traditional Giolitti's Gelateria just round the corner.
What else? Trajan's Column is fab, and the Column of Marcus Aurelius just of the Corso well worth gawping at on the way to the Trevi Fountain (which mustn't be missed), along with the Piazza di Spagna and the Spanish Steps.
If you're into weird and wacky stuff, the church of Santa Maria dei Cappuccini on the Via Veneto has crypt decorated in seriously bizarre way, with the bones of deceased monks.
A catacomb? Most of the best known are on the Via Appia, but there's the lovely catacomb of San Agnese on the via Nomentana.
I spent a lot of time in Rome in the late 80s and early 90s, including living there for a year. It is a wonderful city. Have a great time!