Centro, located on Santa Catarina island (just over the bridge from the mainland), is an excellent starting point for any night on the town or a bite to eat in a variety of formats. This is also where you'll find a good number of cultural areas (like the mercado municipal), making it a good district to explore on foot for half a day or more.
There is no one street in particular where the good times are always known to roll, but the few blocks of Avenida Prefeito Osmar Cunha near its intersection with Avenida Rio Branco provide a bunch of quality choices (i.e. great dance music at Concorde Club and the good beer and bar food of Botequim Floripa). For something over-the-top, check out 1007 Boite Chik on Adolfo Konder; for local rock music, Blues Velvet Bar on Pedro Ivo will be your style.
A great range of cultures is represented in Floripo's downtown selection of restaurants, whether you have an Asian food persuasion (great sushi at Taisho), a cafe hankering (try the short Rua Vidal Ramos and the streets nearby), or want to pick through the deluge of Brazilian restaurants centered near Rua Saldanha Marinho. The good news is that food is generally cheaper here than in other cities in Brazil, so you can enjoy local favorites without having to dig too deeply in your pocketbook.