If you want to visit an outdoor market while in Rome, the most convenient one is Campo de’ Fiori, right in the Centro Storico, near Piazza Navona. The square’s name literally means “field of flowers,” and you can buy them all day and into the night at one end of the piazza. I love the inscription on the simple old fountain where the flowers are sold, which reads “fa del ben e lassa dire” (do good and let them talk). But the real energy of the piazza is brought in the mornings, with a large vegetable and fish market that is there most days until around 2pm.
You will be watched over as you shop by a large, appropriately intimidating statue of Giordano Bruno — a philosopher who was burnt alive for heresy on this exact spot in 1600.
In addition to vegetables and fresh produce, you can pick up spice mixes for dozens of different sauces and dishes (arrabbiata, diavolo, bruschetta, ecc.) and I often saw a truck selling fresh pasta, including in the fall a really delicious pumpkin ravioli (ravioli di zucca).
In the many side streets jutting out from Campo de’ Fiori you can find tons of places to get a panino or piadina to go, or sit down to lunch, if you work up an appetite looking at all the food in the market.