I have been in Rome for this month, and took the metro, then train to Tivoli, Ville d' Est, near Villa Adrianna. The bus trip was a bit difficult, the previous bus broke down and we picked up all of their passengers. Hot, and crowded for sure. The Villa was a beautiful site, lots of fountains and tourists, but take your time and enjoy if you go. Locals were very helpful!
I most highly recommend a visit to Ostia Antica, use Rick Steve's directions and audio guide, terrific! Take the Rome metro to train at Pyramide (all one ticket), and just relax and enjoy the 30 min train ride to Ostia Antica. Rick's directions are perfect. Plan the whole day, do the site for the morning, and then take the train the toward Lido and spend the afternoon and early evening at the beach! Plan to rent chairs, or a chairs with an umbrella for a fee of about 20 euros and have fun with your family. I believe there is a free beach there too. It is lovely, relaxing, and fun, very romantic too. I went swimming, they have lifeguards! The gelato is wonderful. Then the 60 min ride back to Pyramide stop is easy, then catch the metro to your stop in Rome.
Rick was right about the Museum in Garbetella near the metro stop, it is a great place for kids, mine are grown, but it is a museum
in an old but cleaned up power plant so the kids can see the inner workings of the plant. Then go to see St Pauls in San Paolo.