Susan is right: Cul de Sac for lunch, not dinner. Good for aperitivo also.
We love Pizzeria da Remo, Pizzeria Dar Poeta, and Pizzeria La Pratolina. Reservations required at the last one. Call a couple of days early.
For non-pizza:
Taverna Rossini will get you out of Rome Central and into a neighborhood.
In Prati (same side of the river as the Vatican), SiciliainBocca is very good and also out of the tourist fray.
If you are not sure about public transportation, taxis are cheap so use them to your benefit and get out of the center.