Well, if you like natural attractions, definitely see the Iguaçu Falls. I'd go back there anytime instead of Sao Paulo. You can fly to Foz do Iguaçu from Sao Paulo on a domestic flight, cross the border to Argentina and continue from Puerto Iguazu to Buenos Aires again on domestic flight, it may be cheaper this way.
Going to Manaus from Sao Paulo is a long trip and backtracking, if you come from the north. It's worth it, but if you go to a hotel in the jungle (which are usually reachable by boat, so adds to the time). 2 nights at the hotel will be OK, if you don't have enough time. Definitely see the meeting of the waters if you are interested in the Amazon. If you want to see wildlife, I'd suggest the Pantanal instead of the Amazon.
If you see Rio and Buenos Aires, you can totally skip Sao Paulo without losing anything IMO (you have to connect there, but can use an airport hotel to avoid going into the city and the traffic associated with it).