Originally Posted by VidaNaPraia

Here's what I would do:

I'd go to the falls either on arrival (if you can stand more hours of airport and planes) or in the middle/mid-week. Not at the end; too risky to miss int'l flight.

The first afternoon after arrival at the falls, I'd spend the time on the Brazilian side. You can leave your luggage either at the airport or at the park entrance. Both have lockers. I takes a few hours to walk the path and take photos.

Then get a taxi to Argentina. It's safe, even in the early evening. Get a late check in at the Sheraton. Spend day two there on that side of the park. Maybe taking a boat ride under the falls.

Day three, taxi or bus back to Brazil and see the Bird Park (near the park entrance) before your flight leaves. Again, you can leave luggage at the park entrance or at the airport, which also is not too far.

Ideas for Rio:
www.ipanema.com
That gives you two weekends to enjoy some of the famous Brazilian music rhythms in Rio. Try Carioca da Gema or Scenarium, and/or find a samba school rehearsal or feijoada lunch to attend.
And it gives you time for the weather to clear if it isn't cooperating at first to go up to the Christo or Sugarloaf.
If you want more ideas, post.