For a good relatively inexpensive restaurant in the Jewish Ghetto you should definitely try Al Pompiere. It's informal and the food is delightful.

Al Pompiere
Via Santa Maria dei Calderari, 38
Tel. 39 06-686-8377

Another option, if you are feeling adventurous is Checchino dal 1887, which serves traditional food that incorporates some obscure animal parts such as intestines, feet and tails into surprisingly wonderful dishes.

Checchino dal 1887
Via di Monte Testaccio, 30
Tel. 39 06-574-3816

Finally, be sure to consider Checco er Carettiere a very comfortable restaurant by the Piazza Trilussa in Trastevere.

Checco er Carettiere
Via Benedetta, 10
Tel. 39 06-581-7018

You will need to make reservations at any of these places as they are popular in their respective neighborhoods.

Quite some time ago, in connection with the Extravigator.com discussion entitled "Best Restaurant Experience," I provided a link to an article by Mimi Sheraton which discussed a number of restaurants that she felt were so extraordinary that they were worth getting into an airplane and flying to, just to have a meal there:

http://travel.nytimes.com/2009/04/26/travel/26personal.html

One of those restaurants was Le Meurice, which I discussed in another Extravigator.com discussion entitled "France's Finest Restaurants." Another restaurant that Ms. Sheraton listed in that same article was Ristorante Matricianella, in Rome. We are in Rome right now and we dined at Ristorante Matricianella last night. Following her advice, I had the Carciofo alla Giudea, followed by the Bucatini alla Amatriciana and the Tripa alla Romana. The meal was absolutely delicious and the cost was about one-tenth that of having dinner at Le Meurice!

We are still in Rome and enjoying our vacation in Italy immensely. One of the restaurants we've dined at during our many visits to this charming city is Colline Emiliane, which specializes in Bolognese cuisine and is located at 22 Via degli Avignonesi, and its telephone numbers are 06 481 7538 or 06 48 02 80 70. We just love eating there. It had been recommended to Donna Elena and me years ago and was described to us as "the best pasta restaurant in all of Rome." I would say that, if it isn't the very best pasta restaurant in all of Rome, it certainly is one of the best. The prices at Colline Emiliane are quite reasonable. It isn't a fancy restaurant. Reservations are a must - there never seems to be an empty chair in the establishment after 8 p.m.

There are some good restaurants in particular qnad qaint districts of Rome, such as Trastevere and Testaccio..the original Cuisine of Rome, with that particular Jewish touch :-)
I found something about Trastevere and Testaccio restaurants on http://www.rome-explorer.com/rome-guide/Testaccio_Restaurants.html and http://www.rome-explorer.com/rome-guide/Trastevere_restaurants.html

One of the other restaurants that we visited while we were in Rome, during our trip to Italy last year, was Ristorante Canova Tadolini. Some of our Italian friends invited us to be their guests at the opera one night and, a few evenings later, we reciprocated by inviting them to be our guests at this charming, very unique restaurant:

Ristorante Canova Tadolini
150 A/B Via del Babuino
00187 Roma
Tel: 06 32110702

The restaurant is, in our opinion, one of the most interesting dining spots in all of the Eternal City. Its origin can be traced back to the 1800s. Located in the Museum-Atelier Canova-Tadolini, it once was the actual studio of the famous Italian sculptor Antonio Canova and, thereafter, was occupied by one of his highly-regarded proteges, Adamo Tadolini. Today, the studio serves as both a museum and a fine restaurant. Where else can you enjoy wonderful Italian food and wine, dine by candlelight, and also be surrounded by sculptures and works of art that go back to the 19th century?. We enjoyed Ristorante Canova Tadolini immensely (especially the pastas) and we recommend it highly!

The well-known chef Filippo La Mantia recently opened his new restaurant in Rome, which is located in the Hotel Majestic on Via Veneto:

Ristorante Filippo La Mantia, Hotel Majestic,
Via Liguria 1; (39-331) 785-8542; filippolamantia.com

The restaurant was recently featured in a comprehensive article on dining in Europe in the New York Times:

http://travel.nytimes.com/2010/04/18/travel/18Rome.html?scp=3&sq=Dining%20in%20Europe,%20High&st=cse

http://www.filippolamantia.com

My wife and I have been to Italy over ten times now and we've stayed in Rome almost every time we've been there. We thought we knew most of the great restaurants in the "eternal city"; but a friend of ours recommended one that we hadn't heard of - Il Pagliacio. We were in Rome for 12 days on this trip, so we thought we would try it out. Well, here's the essence of our experience there. We each had the 10 course tasting menu, at 140 euros each. The bill came to 306 euros in total. The atmosphere was very nice. The service was friendly, attentive and efficient. The music was tolerable. But the food was skimpy and tasteless. Billed as "fusion cuisine," it lacked clarity and at times tasted strange. Ingredients were mixed together that simply didn't work with each other. Considering the prices being charged, it was simply a terrible experience. Of course, if you know your opera, you know that "Il Pagliacio" means "The Clown" in Italian, and in the most famous aria in that opera, first made famous by Enrico Caruso, there is the utterance "laugh clown laugh." Well, perhaps the owners of the restaurant are laughing at us, the customers, for thinking that we are visiting a fine restaurant. The average hosteria in Rome serves better food than you'll find at "Il Pagliacio."