What you should do in Rio!
When visiting Rio in a short period, here's what you shouldn't miss in our oppinion!

Beaches & other places
The nicest beaches are:
Ipanema (you should try to stay at this neighborhood because of security), Posto 9
Leblon
Copacabana
nicest sunset at Arpoador
Also visit the Cristo Redentor, Corcovado
& the Pão de Açucar (close to sunset time)
Don't miss the Botanical Garden
or the Parque Lage
The restaurants in Leblon and Ipanema are usually very good, Trip Advisor :)
Near Rio you should see
Ilha de Pacetá
Petropolis
Paraty
Trindade