Corcovado: Absolutely Amazing. We paid a taxi driver $30 and he took us around all of Rio (from the hotel to Corcovado to all the beaches, etc...) for the WHOLE day.
Sugar Loaf: Didn't do it, but the gondola/tram looked like it might be cool if you are into that sort of thing (sounds like maybe you're not)
Beach: Don't bring anything other than shorts, literally. Anything not attached will get stolen (including your room key and the rest of your items!)
Chicks: Walked by a bar about 10pm and it was like nothing I have ever seen. The place was packed and there wasn't one single guy in the whole joint. Just all women squeezed in there like sardines looking out the large open window, door way, etc., waiting for some attention.
I recommend NOT wandering around - like at all. I live in NYC and my gf is Brasilian, and I gotta say that I felt really vulnerable there. If you really want to see the third world, there are tours that you can take to the Favelas. Personally don't find that kind of thing attractive. I mean in some sense it's facinating (think City of God), but being someone who loathes tourists in my own town I can't even imagine what people in those places think when a bus load full of foreigners rolls through snapping their pictures.
I don't know where you're from, or if you've traveled much abroad, but the 3rd World is a lot different than what people in the Primero Mundo are used to. I mean, if you're staying at the Copacabana Palace, Caesar Park in Ipanema, etc... you prolly won't notice a difference. But staying anyplace else could result in an experience outside your comfort zone.