Thanks to Peter Pastan, famed DC Chef Owner of Obelisk, 2 Amy's and Etto for the names of his two favorite restaurants in Rome.
Check them out!
http://www.trattoria-romana.it/da/perilli/
and
http://www.ristorantecesare.com/eng/home.php
I have no doubt these are very special places with a referral from Peter, it goes without saying that he knows food, especially in Roma!