This list of restaurants is very old by now since I was there in 1999; but many of these were very worthwhile and will self sort depending on where they are staying, was compiled by several people who lived in Rome in the 90's:
PierLuigi, 686-1302, Piazza D. Ricci , 144 (near Palazzo Farnese) Great fish, you can sit outside, reservations are usually needed to get a table outside. Closed Monday.
Da' Giovanni, Tucked in the north corner of the Piazza Farnese (to the right facing the palazzo) on the side street leading toward the campo dei Fiori. Friendly and very Roman, great wines, food good as well. Real family operation.
Antica Taverna da Paolo & Michele; Via Monte Giordano, 12; 06-68-80-1053, Open all the time, inexpensive, good Truffle Ravioli, off of Governo Vechio, behind SM della Pace
Pollarola, Pza. Pollarola, bet. S. Andrea della Valle and the Campo dei Fiori. Another one that has been around for a long time. Closed Sunday.
Ristorante del Teatro del Grotto di Pompeo, sort of in the same piazza as Pollarola on one of the streets into Campo dei Fiori. Linguine al Raddichio is really good. Good grilled fish too.
Gigetto alle Colonne, Via d. Portico di Ottavia, next to the Theater of Marcellus in the Ghetto. Delicious. The Artichoke al Guidea is wonderful.
Dar Poete, Vicolo d. Bologna off p. SM della Scalla, reservations recommended. Pizza, great bruschetta
da Baffetto, Via del Govemo Vecchio, not far from the Oratorio dei Filippini, the best Pizza in Rome, but get there by 7 pm or you'll stand on line for an hour.
La Rustichella, Vicolo della Cancelleria, 13 (06) 68 80 37 86 (closed martedi)
Pizzeria Nuovo Mondo, Testaccio, This neon lit pizzeria is always packed with locals of this traditional residential neighborhood at the foot of the Aventino, know as the pottery district in Roman times, now the place for clubs and theaters.
Pizzeria Ivo, V. San Francesco a Ripa 158, no nonsense dining in Trastevere at its best.
No-name bakery in basement at 27 Via Barletta nr. Ottaviano Metro. Good. Cheap.
Evangelista, 687-5810, west of the Via Arenula off of the Lungotevere. Excellent, excellent, excellent. Pricey but worth it. Do not order unless you have the specialty, and appetizer called Carciofi al matone, basically artichokes smashed and cooked between two hot bricks.
Vecchia Roma, in Piazza Campitelli. Elegant outside dining, also a little more expensive.
Dittamano, 687-1626, (Piazza Cancelleria, 74) Near the Campo dei Fiori, off the Via Bauliari, the little street that goes towards the Pizza Cancelleria, Very small place. Not very expensive, a great place to eat. Everything is delicious, everything is made fresh that day. They have things that you have probably never had. And their deserts are great, especially the little ice creams.
Trattoria dal Cav. da Gino, Vicolo Rosini 4, 687-3434, North of the Pantheon in a little alley off of the Via Campo Marzio. where all the Parliament guys dine. Small place that has been there for ever, at least as long as Gino, who still serves meals. Try the Tonnarelli w/ peas and proscuitto or the Abbachio (if you like lamb)
Ristorante al Callarello, Via S. Salvator Rosa, 8, 5747575. On the Picolo Aventino. Outdoor seating, need reservation, great seafood, lovely spot to eat out.
Hosteria Umberto, Via di S. Giovanni in Laterano. A little place, not much frontage on the street., on the right going away from the Coloseum. We love the Spaghetti all' amatriciana bianca (A roman pancetta cooked in oil, black pepper on spaghetti with parmesian.). Great for lunch if you are near the Coloseum or the Forum or on the way to Saint John the Lateran.
Trattoria Perilli, Via Marmorata, 39 57424215. Closed Wednesdays. Real typical Roman food. Been in operation for a long time.
Il Vascello, it's not too far from the American Academy in Rome and is frequented by the fellows as well as all the locals of that residential district, Monte Verde Vecchio.
Pizza, Ice Cream, Coffee, Cheap Meals:
Viccolo del Grotto,. Great Pizza. Try the Fiore di Zucca (Zucchini flowers, if they are in season.) or the Gorgonzola with rughetta (Bianca, no red sauce)
L'Insalata Rica, V. del Paradiso, alongside the flank of the S. Andrea della Valle. Salads and good pastas, they have a pretty good Spaghetti alle Vongole. They have another location in the Piazza Pasquino, both locations you can eat outside. Great for lunch.
Sant' Eustachio Cafe, In Piazza Sant' Eustachio, in the Pal. Maccarani. Extremely good. Beware if you order a coffee it will come with sugar in it. If you don't like sugar order, senza zucchero.
Bar Camilloni in Piazza Sant'Eustachio across from the church. Also good coffee, and they now serve great lunches, with fresh pastas each day and various other delicious "fast meals."
Tazza d'Oro, 678-9792, (Via d' gli Orfani, 84) just north east of the Pantheon. The best coffee in Rome. If you dare, try the Granita di Cafe with layers of frozen coffee granules and whipped cream!
Giolitti's, Via. d. Uffizio di Vicario, north of the Pantheon,. Ice Cream, lots of choices.
Bar Pica, Via dell Seggola,12, off of the Via Arenula to the west, before you cross the river. In my opinion the best ice cream in Rome, I try to keep this place a secret, so don't come back and disappoint us by not going several times!. Try the Riso, which is like rice pudding only ice cream. All the flavors are delicious.
Cafe
(forget the name), in Pza. S. Lorenzo in Lucina, on north side of Piazza. Tables outside, they have great sweets inside, nice place to sit as alternative to all the usual spots.
Bar Tre Scallini, Piazza Navinna. Have the Tartufo, A chocolate lovers delight.