What a great stay we had at Maison Ana! If you want to feel like a local, stay here. It is one of the best Airbnb experiences I've ever had! The place was safe, clean, comfortable and close to all Rome has to offer. There are lots of little markets close by to stack up on staples and cook in the well-stocked kitchenette. I'm sure that there is a trick to the hot water in the shower that I never quite figured out, so you may want to ask about it during the introductory tour of the apartment.
We found a great place called 320 Gradi a few blocks from the apartment. It wasn't fancy but the meal and the hospitality were the best we had during our 5 days in Rome. ("You don't like, you don't pay!") It is true what all the guidebooks say. Avoid the restaurants in the touristy areas, especially the ones that have people outside handing you menus. Instead, find places filled with mainly locals.