Campo de Fiori is a piazza a short walk west from Largo di Torre Argentina and not far from the larger Piazza Navona. This is a part of Rome that many tourists enjoy:  during the day, the square is filled with vendor stalls.  If you're looking for it, it is likely here -- vegetables, fruits, olive oils, housewares, hats, perfumes, meats, T-shirts, flowers and much more. You can enjoy a leisurely stroll browsing the stalls and watching locals buying food for lunch or dinner. 

At night, the stalls disappear and it becomes a social event.  Many restaurants line the piazza, some of them quite good and more reasonably priced than what you may find, say, in the Pantheon area.   Plus street muscians play in front of the restaurants, which creates a very "Italian" experience.   You can sit, listen to the music, and enjoy your drinks and food.