i want to visit all i can of course! i want to go to the beaches, and i also want to visit the pao de azucar and the cristo! and we are ging to go out at nigth. I need to stay in a place where i can go to everywhere easily.. and not so dangerous!
I believe that staying at "zona sul" (I mean: Flamengo, Botafogo, Copacabana, Ipanema or Leblon) is the best choice for you, because these neighborhoods are close to Cristo, Pão de Açucar and also most of the parties. They are also some of the "wealthiest" places in Rio.
About Centre, I wouldn't stay there because it's not nice at night and is really crowded during the day... It's more like a business centre.
Barra da Tijuca is a bit far from the other places, you might need to speed a lot of time in the bus or some money to go to other places.
So, I'd say Copacabana or Ipanema are the best places for you. They are also close to the subway and to the "Lagoa Rodrigo de Freitas", that is a really nice place.
I recommend you to see the sunset from the Arpoador, in Ipanema (it's one of the most beautiful things I've ever seen... people applaud the sun when it sets!)