Sumptin' Del Medio, Havana
The best thing to do at night in Havana is to search for random little bars, avoiding the tourist traps such as Boguita del Medio (sumptin' like that) where drink prices rival that of an American city (and everyone inside is Canadian or European). [note- Cubans aren't even allowed in the tourist bars; A Cuban friend actually snuck in with us by pretending not to speak Spanish with an exaggerated American accent.]
Dress Code: None that I noticed. Cubanitas are typically half-naked.