My (now) husband and I spent months in South America a few years ago and we celebrated New Years here in Rio de Janeiro. It's a vast and stunning city. This is an image of the view from the Sugarloaf Mountain - you can take a cable car up to the summit. From the top, you'll be able to enjoy 360-degree views across the sprawling city below, Guanabara Bay, Copacabana Beach and up to Christ the Redeemer statue.
The itineraries you can take from Rio are amazing and so diverse. Have you ever looked up Iguazu Falls?!