I have been to Brazil a couple of times. Amazing place. Rio is not really a favourtie, although it is quite a beautiful city to look at. Especially from the air flying into SDU on a beautiful sunny afternoon. Probably the most spectacular landing approach I've experienced. Stunning!
When Rio was announced as host, I said to myself, what the! Its a choatic city on the ground. I thought about going, but other plans have taken precedence. Rio itself, I never felt threatened. Some areas obviously I would not go to. Most Favelas and some of streets just behind the main tourist areas. Copacabana, Ipanema are obvious, but areas like Sta Helena are stunning.
If you are going to Brazil, do the Olympic thing, but spend some time outside Rio. Sao Luis is a fav. Recife and Salvador are brilliant. Head to Iguazu Falls, which is amazing. The city itself is not the safest or endearing place in the world, but worth suffering just for the falls. Manaus on the Amazon is a crazy hive of activity set in a quite spectacular setting. Porto Alegre is also worth it, if only to experience a totally different Brazil.
Olympics or not, just go!
Oh! remember to get your visa first! And I've found Brazilian immigration can be kind of abrupt. But, just be polite, yes sir, no sir is the right approach.