I've been to Rio twice and didn't much like it. Not a lot to see - beaches that you can't take anything but a towel to (or it'll be stolen), the statue of Christ, the botanical gardens... that's sort of it. But if you speak Portuguese, that'd put it for you ahead of the rest of South America, which mostly speaks Spanish. However, Manaus way up the Amazon is worth a visit; so is Salvador on the coast. Brasilia has interesting modern architecture.
But personally I thought Buenos Aires was much more interesting. You can see Iguazu falls from either the Brazilian or Argentine sides but I think the Argentine side is better.
Peru for the ancient sites, specially Machu Picchu, and Cuzco as a fine colonial town. Lima's nothing special. The train across the altiplano to Lake Puno is wonderful.
Colombia: Bogota was also nothing really extraordinary but Cartagena is pretty.