Thanks for the tips guys. We're going to Lollapalooza in Sao Paulo one day which is difficult to plan around. So far it looks like:
Day 1: Arrive Sao Paulo but get on a plane immediately to Buenos Aires (arrive 5 pm)
Day 2: Buenos Aires
Day 3: Buenos Aires and depart for Manaus around 2 PM
Day 4 & 5: Manaus - probably will arrange something with a tour guide
Day 7: Manaus all day and depart for Rio at 5 pm
Day 7 - 10: Rio de Janeiro, depart for Sao Paulo 9 PM on 10th day
Day 11: Lollapalooza
Day 12: Early morning flight to Foz, see the falls
Day 13: Iguaçu Falls and return to Sao Paulo late flight
Day 14: Sao Paulo all day then flight home at 10 PM
I would have preferred to do Foz immediately and go to Buenos Aires through the border there but unfortunately I couldn't get any flights that would work (assuming 1:20 Intl to domestic connection GRU wouldn't be enough).
Definitely will look into day trips to Petropolis or Niteroi.