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.
Villa Giulia Museum We saw this...I think. I just looked at a photo of the building and asked my wife. She said we were there. It was 15 years ago and has become a kaleidoscope of things that double expose one another in memory.
My brother encouraged us to get to Ostia. Sadly, we just ran out of time.