I don’t think I’d bother with a guided tour in Rome, except for maybe the Vatican Museum.
My wife and I spent 5 days in Rome about a year ago, and saw the following:
Colosseum
Forum (original & Trajan’s)
Palatine Hill
Vatican Museum
St. Peter’s (inc. papal tombs in the grottoes)
Basilica of St. John Lateran
Piazza Navona Xmas market
San Luigi dei Francesi (has a bunch of Caravaggio art) - a block or two North of Piazza Navona
Santa Maria sopra Minerva (has a Michelangelo, and is only Gothic church in Rome)- literally around the corner from the Pantheon
The Pantheon
Church of the Gesu (home church for the Jesuit order) - on way between Pantheon & Forum/Colosseum/Capitoline Hill
Trevi Fountain
Spanish Steps (as part of an afternoon of shopping on Via del Corso/Via Condotti)
Piazza del Popolo (after shopping)
Basilica de San Pietro in Vincoli (has Michelangelo’s Moses; also supposedly has the chains used to bind St. Peter, hence the name)
The Forums, Palatine Hill and Colosseum are literally within about a half-mile of each other. The Pantheon is maybe a mile away, and Piazza Navona and all the other nearby stuff isn’t very far from it.
St. John Lateran is really impressive- it’s literally the Pope’s cathedral. In other words, as Bishop of Rome, it’s his home cathedral, and where his “cathedra” or seat is, not St. Peter’s.
I highly (HIGHLY) recommend the Rick Steves’ books; they give you excellent maps, stellar restaurant recommendations, and nifty little local tips. Having used Fodor’s, Frommer’s and Lonely Planet in the past (London, Budapest, Prague, Paris, & Florence), the Rick Steves’ books are by far the best.
And don’t be a chump and eat McDonald’s. Italian food isn’t what you’ll necessarily think of as Italian food, but it’s definitely terrific, and worth getting. In Rome, I’d recommend getting anything with artichokes (carciofi - said “car-CHO-fee”) and go out of your way to get pasta alla amatriciana. Both are local specialties and will knock your socks off.
Another recommendation is to get gelato. I really liked San Crispino gelato near the Pantheon, but there are lots of good places around.
Finally, don’t eat anywhere with pictures of the food; they’re assuredly tourist traps with substandard food. If you get the Rick Steves books, they’ll recommend you good, authentic local places.