The oldest market of Rome is held on the Piazza di Campo de’ Fiori (flower market). There is a daily market where you still can find flowers, but also much more. Spices, pasta, olive oil, … and cheese.
The square is surrounded by a lot of bars and restaurants. But if you are hungry, skip the restaurants and go straight to the corner of the market, where you can find a bakery named Forno Campo De’ Fiori and taste the Pizza Bianco.