Here they are:
Dino & Tony's Hostaria - Pizzeria
Via Leone IV, 60
This restaurant was actually recommended in a guidebook, although not under the restaurants section. It was a little sidebar in the Vatican tour section of Fodor's Pocket Rome guidebook. They recommended this place as a good alternative to the touristy places right across from the Vatican museums. They were right.
I've been here several times for lunch while visiting the Vatican. Both times have been superb, with great service and good renditions of basic Italian food. Don't expect to get a menu; the waiter just brings good food, like rigatoni bolognese, etc. Expect a bit of a language issue, since the waiter doesn't speak English; bring a dictionary and make do. Spanish should also work, since the waiter is from Argentina.
You're in Rome, so don't be in a hurry, and just have a leisurely lunch while they bring you food until you've had enough.
Il Pancrazio
Piazza del Biscione, 92
This place is in a little square right off of Piazza Campo dei Fiori. If you stand at the statue of Giordano Bruno, turn to his 5 o'clock and head out the Piazza through that corner. The restaurant is in the little square, just on the right.
The food is pretty good. It's not the cheapest, but you'll get a good meal for the price. Check out the desserts -- there's a cake with layers of thin chocolate on it. Closed on Wednesdays. May want to have reservations on summer nights.
Est!Est!Est! (Antica Pizzeria Fratelli Ricci)
via Genova, 32
I've been here a couple times. A good choice if you're in the area. Decent dishes, you will not be disappointed.
No 39.
Via Palestro
This restaurant has a number in it's name. This is a basement level restaurant on Via Palestro between Via Gaeta and Via San Martino della Battaglia (near Termini station). I wasn't impressed by the main dish, but I did get to taste a bite of the Tiramisu. It was the best Tiramisu I've had in my entire life. Hands down. We tried to go later just for dessert but it was "feenished". It's worth the trip for the Tiramisu; maybe lunch, before it's feenished.