Any suggestion for moderate and inexpensive restaurants in Rome? We don't want to go to tourists traps, we would like to eat where italaians eat. Thank you!

We like Ai Marmi in Viale Trastevere or Remo in Piazza santa maria liberatrice for pizza approx 12 euros pp for a meal.

"We don't want to go to tourists traps, we would like to eat where italaians eat."

Reminders, but you probably already know this:

Avoid places with plasticized menus in English.
Avoid places that have English menus posted outside.
Stop a businessman eating a panini as he walks down the street, and politely ask him where he got it.

Be aware that after you go to the place the pizza eating businessman sends you, they might try and push off an inferior piece on you. This happened to me alot and I noticed that it happened to other tourists as well. If you notice, the Italians will not accept a piece that is inferior and will have the counterperson cut them a new cut. Do it too and then ask to have it heated for you. Pay the cashier and then show the receipt to retrieve your pizza or calzone.

Sometimes it is very hectic in those places and you might be intimidated like I was, but the food is usually good. It is better to chose one that is busy with a better turnover so to speak.

Thank you very much to all of you for the suggestions)

Two places we really enjoyed on our last trip. Both are in the Piazza Navona area. The first one, easy to find is Ristorante Tre Archi on via dei Coronari 233. The place is tiny and has amazing food. The second is in the maze of back alleyways but look for it; it's Antica tratttoria La Scaletta on via dell Amina. Again, small but packed and for a good reason. I can't wait to eat at both places again.
Let me know if you try either one.

I love Mario's in Trastevere on via del Moro. Great food at reasonable prices, small and homey.