Arcos da Lapa
If you are coming to Rio for the first time, you'll probably find interesting taking a look at the flyers distributed at the hotels, full of touristic places to go. But don't. Some of the places yes, are worth seeing, but maybe only 10% of them.
At Lapa you will find the true Rio de Janeiro. That historical neighbourhood, is surrounded by bars, restaurants, danceclubs and alternative places. There you will find all the tribes of Rio. The hip hop boys, party girls, rockers, skaters, samba lovers, capoeiristas, etc.
Just avoid walking alone during the day, because the police isn't around in general and it's a desert/dangerous area.