Navona Notte, near Piazza Navona, is one of the best places in the centre for good quality and price.

In Trastevere head for Piazza San Callisto, and the pizzeria of the same name which has the biggest pizza in the city.  The price is reasonable, and you won't have to eat again for the rest of the day.

For a sandwich Aristocampo in Campo dè Fiori isn't bad. 

If you are really on a budget, but want a drink with dinner follow the street behind the church of Santa Maria della Pace until you come to a small piazza with a bar in it (its the only thing there).  For the price of just one drink you can help yourself to the buffet that is served between 7.30 and 9.30 and includes pasta, rice, dips, bread, veg etc. then you won't need dinner.

Another cheap place to eat is in Parioli, and it's called Il Simeto (it is in Via Simeto!). It could seem a bad restaurant (old fashioned, small, the owner could even be rude), but food there is more than delicious: very large portions of pasta, good meat courses, and a wonderful pizza, all at a very affordable price.

A very good cheap place is close to Termini Station : called Sfizio Pizza in Via Giovanni Giolitti 77 corner of Via Gioberti. Menu items are  between 5 to 15 Euros. Very good Pizza, Lasagna, Chicken and they have also English breakfast for the morning.

Great German and Italian food with excellent beer can be found at the Italian brewery, Birrera Peroni, near Trevi Fountain.

Termini Station itself is a good and cheap place to eat. A self service buffet, usually stocked with fresh meat and vegetables, salads and fresh fruit salads. Wine is also self service, you can fill up a carafe of red or white from a barrel. Its very handy if you have problems ordering off a menu in Italian!!!!

For a cheap lunch with great views, climb the steps at the Vittoriano Museum Complex and eat at the cafeteria there.