^i don't know if there are better places in the more residential areas, but just off Piazza Navona there's a street, Via del Governo Vecchio, with 5 or 6 thrift stores with good inventory (particularly if you like Barbour coats, oddly). Also a great little hole in the wall for ties. Prices are a little elevated though, in comparison to US thrift stores.
+1 on Via del Governo Vecchio. Bought a nice hat for myself a few years back and was similarly amazed by the variety of Barbours on offer. Follow your nose - the smell of old wax will lead you to the right shop. Most of what's on offer on the street, though, is similar to what you might find in a vintage shop in the US - 70s fashions, denim jackets, etc.
There's also a pretty good lunch place on that street - maybe Corallo? Get the carbonara. (5 minutes after we were seated it filled up with models from a nearby studio. In Rome, the models eat pasta.)