Since Mitch asked (it doesn't take much to get me going). Several years ago, in Rome with Rich & Peg for a few days, we all went to Checchino dal 1887 and Perilli, both in Testaccio. The food (& the room) at Perilli is no frills basic restaurant box and the service can be less than friendly unless you make an effort to break the ice. However, Ginny & I have grown to love the place and have now been back probably 4-6 times. I especially love the rigatoni con pajata (look it up) there. Checchino dal 1887 is a more upscale place, noted for its incredible wine list at very reasonable prices. Yes, the wine was excellent, but the food seemed tired and the owner and staff absolutely disinterested. Maybe a bad night, but I didn't get that feeling. Maureen Fant and I think Katie Parla both favor it, but Eliz. Minchilli and I pick Perilli for the food. Another interesting place in Testaccio is Flavio al Velavedotto, which seems to cater to locals. Ginny & I went back a couple of times and had very nice mid-range (actually pretty inexpensive) meals there. It has an outdoor inner courtyard & some limited roof deck seating for when the weather cooperates. They also have a wall of wine bottles and you go and pick your bottle(s) from there. Prices are clearly marked. Great idea, very nice range.
The old market in Testaccio, which we loved, has been closed down and moved to a modern structure. We didn't love the new place. Better markets elsewhere in Rome.