We chose to spend an hour visiting the Roman Synagogue for a different perspective on the city's history.
After paying 3 euros each for a student fare (the normal entrance fee is 6 euros), we spent 15 minutes in the small but impressive museum.
Information sheets are available in many languages to explain some basics of Judaism, as well as the specific artifacts. Most impressive was the vast selection of Torah "skirts."
The only way to see the actual synagogue is on a short tour. Our group was only four people and was led by a knowledgable Italian guide who spoke very good English. We were free to ask many questions and got a good overview of both the history of Jews in Rome and the synagogue itself.
Opening hours are approximately 9am to noon.