To be honest there is not that much partying in Providencia. My favourite place is Rolando's Roots Bar who religiously claims to have life music everyday, which most of the time is not true. Rolando is known by everyone in Providencia and his bar in my opinion is the best place to go.
Besides this bar, there's a couple of places that you might want to try, but you better ask a local while you are there what are the nice places to go at the time of your visit.
By the way, Rolando is now famous becase he appeared on a Colombian reality show called "Desafio 2011" We hope that that didn't affect his ego and cocktail making skills.