I've been living in Rome since I was born (except one year close to Milan), but I guess I'll never get bored of this wonderful city and its amazing quarters...
The one I love? Trastevere all lifelong! It's unique worldwide, wonderful on day-time, but very expecial at night... it's the place I absolutely prefer where to spend my nightlife. It's full of bars and pubs, where you can have fun just walking around the streets and sit down to Piazza Trilussa (always full of italian and foreing guys talking and playing guitars) or stopping to taste some authentic irish beer in the pubs.
If you will ever visit Rome, please stop once at Mr. Brown, my favourite pub. It's amazing, very small (just a couple of tables to sit down) but always full of people. I think it's one of the cheapest pubs in Rome too. I love it under fall : when outside it's terribly cold, there's nothing I'd wish as much as a draught beer of Mr. Brown!
Just the time of a couple of beers, and then you're ready to move and have fun walking around in Trastevere : from pubs to pubs, you can talk, meet people, discover the amazing beauty of this ancient quarter that takes place really in the city-centre.