There is of course not enough time to visit everything, but we at least saw the highlights such as the Coliseum, the Vatican (and its museum), the Forum Romanum, the Spanish Steps, the Pantheon and plenty of other monuments.
The Villa Hadriana was a domain with a large Villa constructed by Roman emperor Hadrian in the 2nd century which he used it as a retreat from Rome. A large domain with lots of interesting things to see.
Again, as with Rome, enough to walk around more than one day.
Except for Rome and Tivoli (with the Villa Hadriana) we also visited some small, typical places in the neighbourhood, all guided by Bart. There was for example the beach of Sabaudia, where also the Romans go, the small village of Sermoneta, Nemi, Castello Gandalfo (where the pope has his residence).