I would recommend four countries: Peru, Chile, Argentina, and Brazil.
Peru: Machu Picchu
Chile: Santiago
Argentina: Patagonia
Brazil: Lençois Maranhenses
There are a lot more places to visit in these countries, since I am more familiar with Brazil I will give you more recommendations from here: Maragogi, Fernando de Noronha, Salvador, Rio de Janeiro (quite obvious), and Foz do Iguaçu.
Also, you MUST visit the Amazon, I've seen some videos and there are good tours from Peru and Brazil.