During the 19th century, Barranco used to be a quiet bohemian and almost melancholic town that was called home by a bunch of mostly artist and merchants; a place nearby Lima that came to active life only on summers, as a beach resort. Nowadays it's still considered as one of the "bohemian neighborhoods" in Lima, if not the main one; but it is no longer quiet nor "romantic". 
Barranco at night — Photo courtesy of Robertt Luna
Currently, in 21st century, Barranco has preserved most of its traditional architecture, and is still home town for many young artists: but commerce and nightlife have also settled here. So, the old bohemian beach town bursts with new life after the sunset, all year round. And has become a great place for doing some bar hopping, since there are places for almost any budget.
A place that prides in serving one of the best pisco sour cocktails in the neighborhood is Huaringas, which is actually located in the border between Barranco and Miraflores, and which is considered as a gay-friendly place; another affordable good choice for drinking, partying and socializing would be El Dragon. And if you prefer some more classy places, you may as well go to Chala Costa Fusion, actually a restaurant but with an excellent and well stocked bar.
However, as you would do in any foreing city, remember to keep your eyes open... and fun is granted.