Well, Brazil is big, so you need to specify which sights you're interested. Beaches? History? Nature?
Rio is an all-world city, with history (a fort between Copacabana and Ipanema, the old presidential palace, the old port, the Monastery in downtown, the Christ) and nature (world-class beaches, the Pão de Açúcar peak and the Tijuca jungle), with a lovely day trip option in Petrópolis (old imperial city, way more warm than Rio); São Paulo is the culture center, with a large and never quiet downtown, our major museum (MASP) and secondary sights (also close to Aparecida, our equivalent of Fátima in a way. The 2nd largest Catholic Church in the world is there, only St. Peter's Basilica is larger); my home state capital, Belo Horizonte, has one UNESCO site (the artificial Pampulha's lake) and tons of pubs and bars, but the huge tourism hub are in the preserved colonial cities (Ouro Preto, Tiradentes, Mariana, Congonhas and São João Del Rei) with awesome XVIII churches and in nature (the caves close to Belo Horizonte and the national park in Santana do Riacho, with dozens of hikes and waterfalls), also in the Brazil's most important Modern Art museum, in Inhotim. All of those are reachable as day trips (Tiradentes and São João Del Rei are the furthest cities, 3h30min on bus); since you talked about the Iguaçu Falls, your friends probably live close to Curitiba. Curitiba has a lot of parks, so, if you're into this, you can spend a day or two there; close to Paraná are Santa Catarina and Rio Grande do Sul, with a strong european presence and Brazil's 2nd favorite winter city (Gramado). Close to the Uruguay border, you have São Miguel das Missões, ruins of a jesuit church, built to convert the indigenous people (and, later, protect them from the Bandeirantes).
Going up and getting warm, you have the northeast beaches, our favorite summer travels. In Salvador, the focus is the preserved historic centre, and the same applies for Recife and Olinda (the Brazilian Venice nickname is not 100% accurate). If you want beaches, you must go to Maragogi, Maceió (both very close to each other, but watch out: Maceió is as violent as Salvador and Rio), Porto de Galinhas (close to Recife), Trancoso and Morro de São Paulo (both somewhat close to Salvador). Porto Seguro is the middle ground: you have historic heritage (specially close to Cabrália, where Cabral "found" Brazil and the portuguese first settled) and 2 amazing beaches (Arraial d'Ajuda and Coroa Vermelha). I'm not a beach guy, so I probably missed some hidden highlights, but those are the most known here. Oh, Fernando de Noronha is probably beautiful as well, but it is really, really, really expensive for us. I don't know how far the dollar goes there, but for brazilians is a prohibitive place, unless you're really rich (or willing to get a huge debt).
Last but not least, the Amazon and the Pantanal. I never traveled to any of those, but I'm aware that Bonito is a common base to explore the Pantanal, but you can also pick a smaller city. You'll need to land in São Paulo or any other major capital (Curitiba can work), fly to Cuiabá or Campo Grande and, there, pick a bus or a transfer to the base cities. About the Amazon, I would recommend staying either in Manaus (you can know Brazil's most luxuous theater, the Teatro Amazonas) or Belém (if you do, please go to Santarém and Alter do Chão. They're so beautiful, and so, so overlooked), or even both, if you can spare a week. São Luís is not so far (on a plane travel) and it's one of the few cities in Brazil with french heritage. Also, close to Campo Grande and Cuiabá (on a plane, again), is Brasília, our current capital. It's a planned city, exotic, but I don't recommend you planning to visit it. With our current political situation, protests are usual and they can turn violent easily in Brasília. Leave it for a more quiet political period