I did Rio, SP and the Falls in 2016. Here are my suggestions.

SP: I stayed at the Renaissance as a top tier Marriott elite. The upgrade (to a corner junior suite on a high floor) and lounge were nice and the location is pretty good, but I'm not sure it would be good value for someone without status. If you're interested in South American modern art, there are interesting museums, including the one in the park that was mentioned in an earlier post and one almost across a big street with a pedestrian overpass that's part of the University of San Paulo. If you like cool modern design, there's a stunning Design Hotel (Starwood brand) that IIRC is close to the park, but apparently isn't on a bus route from GRU like the Renaissance is.

Rio: Aim for Copacabana or Ipenema (spelling?), not Barra (unless you want to treat the new Grand Hyatt as a destination resort), Leme or elsewhere. The Sheraton is in a questionable location, although you need to be very careful even on streets around the (Belmond)Copacabana Palace.

The Falls: Wth two nights, you don't have time to do the Argentina side too. I stayed in both hotels in the park, the Sheraton and the Belmond. I would strongly recommend the Belmond if you can get a reasonable rate. It has nice grounds and the big advantage of having the walkway to the falls start just across the road. You can go early or late to avoid the crowds--hotel guests have 24/7 access although of course you should not try to walk the trails after dark. Don't miss sunset from the hotel's clock tower. The place has a big breakfast buffet, an attractive pool (much larger than the Sheraton), an interesting fine dining restaurant, and historic public areas, plus a couple fancy shops. However, standard rooms are a bit small and definitely four star rather than five star standard. I was charmed by the bird park just outside the park entrance, including having big tropical birds swoop around me in free flight. For this, you take the hotel's shuttle to the park entrance and walk a few blocks away from the park--it's well known and just on the left with good signage.

There's a new hotel association, IIRC called Grand Luxury Hotels, that covers most/all Belmonds (former Orient Express Hotels), among others. It's free to join on line and bookings through them get some limited "status" perks from the very first stay, so you can't lose unless you find a (significantly) lower rate elsewhere.