The peak lunch crowd is at 2, and most places don't open for dinner until 7 or 7:30. There is typically no smoking indoors, and usually the patio seats in Rome are also comfortable without much smoke.
Ar Galleto (also called Da Giovanni), Vicolo del Gallo, 1. Closed Mondays. Open from 7:30 for dinner, but they were willing to seat guests at 7:15. (Meal for family of 4 cost 48.5 E & 79.5 E with wine)
On the Northwest corner of Piazza Farnese - the outdoor seats overlooking the fountain are across the street from the indoor part of the restaurant with a great view of the beautiful Palazzo Farnese. This restaurant was featured on a website www4.colgate.edu/ scene/sept1997/italy.html with recommendations for the involtini, but that was not on the menu in April 2005. This is just around the corner from Campo de Fiori, but is nice and quiet and romantic. Excellent dishes include:
Antipasti romanesque - the best marinated vegetables - especially the narrow purple eggplant
Ravioli with cheese and spinach in a yummy tomato sauce
Roast baby lamb (abbacchio di forno) with a crispy crust, gravy and roast potatoes.
Piccotine al limone - veal in lemon sauce and grilled chicken.
Fried zucchini blossoms - stuffed with cheese and probably an anchovy.
Trattoria Der Pallaro, on Largo di Pallaro (go south on Largo dei Chiavari past the first right turn to the second right which opens onto a small parking area. The restaurant is on the corner and has outdoor seating, enclosed in plastic sheeting. This was recommended by several people on the Slow Travel website. It is a delicious and unique 20 euro per person fixed price five course meal with your choice of red or white wine. They charged a total of 65 E for two adults, an 8 year old and a 4 year old, giving servings of the two appetizer courses, and three servings of everything else. The first course was marinated fennel, green olives, prosciutto, and a yummy lentil and olive dish. The second course was fried cheesey rice balls and fried veal patties. The pasta course was a simple rigatoni with tomato and cheese (similar to Amatriciana but without the bacon). Then there was roast pork with a scrumptious breaded eggplant, small balls of fresh mozzarella (rather bland on their own but were good with olive oil and veal sauce) and homemade potato chips. Desert was fantastic - a honey nectory sip of mandarin orange juice and a ricotta pie with orange marmalade. In the kitchen they also had artichoke cooked roman style (as opposed to fried in the Jewish style) and a deep green sauteed vegetable that may have been the vegetarian entrees. They suggest reservations, but may have seats at 7:30, still early for Romans. Very friendly owners and highly recommended. It is just around the corner from the Hotel Teatro di Pompei.
Ristorante Galeassi on the north side of the Piazza di Santa Maria Travestere, 3, is pleasant. There are street musicians and a nice view of the piazza with its unusual looking fountain. Featured dishes: Roman artichokes, spinach and chicory saute, and penne arrabiata- a spicy tomato sauce. The asparagus looked and tasted awesome - all tender stalks and no bitter leafheads. The puntarelle (curled chicory shavings) in anchovy sauce was bitter and salty. They specialize in seafood, but a light lunch with four vegetables and one pasta shared among a party of 4 was 37 E- kind of pricey.
Tre Scalini in Piazza Navona, to the right of the church of Sant'Agnese in Agone. It has a nice view of the Fountain of Four Rivers, but the gnocchi in roquefort was much too salty, the saltimbocca veal was tough, dry and salty, the service was poor (slow and incomplete, with some dishes ordered never being brought). The fried and marinated vegetable antipasti was good, and the chicken Roman style was tasty, but very small - only a drumstick and a nubbin of backbone compared to the whole small chicken at Ar Galleto. They charged separate fees for bread and olive oil (1.5 E per person for each), and automatically added a 18% tip to the bill. There was also a lot of smoking despite customer requests to be seated away from smoke. Also the ambiance is ruined by tour buses that park in front to discharge masses of people, block the view of the fountain and exude exhaust. Although the bill was one of the highest for 3 people without wine (66 E), the food was so inadequate that it was necessary to purchase pizza at a nearby stand.
Tip: The two places, one in Rome and one in Pisa, that added 15 or 18% tip into the bill were very touristy and the food was not good (so look out for that on the menu and go somewhere else).