My wife and I found there is much to see in Rome in a reasonably small area. We were only in the neighborhood for about 8 days and one of those we spent in Pompeii.
I was also in Rome a couple times in my short Navy career.
I and we barely scratched the surface regarding all the things there are to see there.
Ostia, the ancient port of Rome, can be reached easily by public transportation from Rome. When I went there were a lot of people on the train headed for the beach, but the stop for Ancient Ostia is about a mile before that--the site is an easy walk from the train stop. When I went it was not crowded at all, only a handful of other people there--it has a great collection of well-preserved buildings, like Pompeii without the crowds. Ostia is where St. Monica, the mother of St. Augustine, died.
Another easily-overlooked thing to visit in Rome is the Villa Giulia Museum which includes a lot of fine Etruscan art.