Monte Testaccio. Right in the neigborhood of Testaccio, behind the piramide is one club or bar after another. I don't know if I would go on my own, maybe find a kindred spirit on the tour to come along. Testaccio has some great cheap restaurants as well, it is considered a "true" Roman neighborhood.
Otherwise, try Campo dei Fiori in the evening, or Via del Governo Vecchio, which leads to Piazza Navona. All these places have good restaurants, pizzerias, cafes, or bars. Trastevere in also good, as crowded at night as it is during the day, mostly young people out for a night. Lots of pubs, restaurants, shops, and a movie theater which shows English language films. And remember, Italians (especially Italian men) are very friendly and may try and talk to you. Don't worry, they don't bite! Have fun!