If you find yourself in the Testaccio area try this place - though it’s not for the faint hearted. Very simple and cheap: specialises in offal (the slaughterhouse used to be right nearby).
This is a major part of Roman cuisine but there are dishes that don’t involve brains and intestines. Nervous eaters should avoid anything with the word pajata: it is not Roman dialect for potatoes. Sit under the sycamores and practice your Italian.