There is a market held in Campo de'Fiori Square from Monday to Saturday where you will be able to buy fresh fruit and vegetables, cheeses, pastas and flowers. It has been open for many years and is held in the very centre of Rome near Navona Square.
If you want to blend in with the locals then Campo de'Fiori is the place to go, and the cafes and restaurants which line the square make it a hive of activity both day and night. It doesn't matter what day of the week, this square is always busy and it has also become a popular meeting point for both tourists and locals.