Rome's hottest row of nightclubs and bars can be found on Via di Monte Testaccio (often referred to as simply "Testaccio"), a street that runs alongside the artificial hill of the same name on the Tiber River (also called Monte dei Cocce). The hill itself is unique in that it is made from shards of ancient pottery, while the area has had a festive atmosphere for millennia, serving as a long ago center for carnival celebrations.
Some of the most consistent joints you'll find here include Caruso Cafe de Oriente, Caffe Latino, and Akab Cave. Caruso and Caffe Latino are both hugely popular with people who like the sounds of Central and South America, particularly salsa, or anyone who enjoys dancing the night away to good live music. Akab Cave is more DJ-centered and high-tech in its layout, appealing more to followers of modern electronic music. Just be careful walking by the Tiber, there have been issues in the past with gypsies targeting travelers.
These clubs are only the tip of the iceberg. There are plenty more along this and perpendicular streets; if you're not sure where to go or you need to accommodate some diverse tastes, take a stroll along Monte Testaccio. You'll find something to pique your interest.
Note:You'll also find a handful of exceptional restaurants in the greater Testaccio district if you're one to avoid tourist centers and attempt more authentic gastronomy. Try the pizza at Rema (Piazza Santa Maria Liberatrice), the local atmosphere of Flavio al Velavevodetto's (Via di Monte Testaccio), or the consistent flavors of Felice a Testaccio (Via Mastrogiorgio).