So you have 10 days to visit all three places?

IGU could be done in a day or two if you wanted to push it...one full day exploring the Argentine side of the falls and half a day on the Brasilian side. IMHO, the Brasilian side has the better views, but the Argentine side is more fun! Perhaps you could fly from GIG to IGU, see the Brasilian side, spend the night on the Argentine side, and the next afternoon fly on to AEP from IGR. That would leave 4 days in BsAs and Rio each.

For Rio, my visit was four days. Stayed in Ipanema...first day hung out there and walked around the neighborhood (then went to Lapa for the evening). Second day did an all day bus tour (night out in Leblon). Third day more relaxing by the praia (night in Copa), then last day walked around Urca and other areas (although I was hoping to tour Isla Grande). I'll let the locals discuss Buenos Aires.