[El Viajero]

Its really just a matter of plugging in the dates on all of the airline websites that fly from the airport and being creative. It would make sense to check on flights that fly to the U.S. But if that still does not get a cheap flight then start experimenting with flights to other location in Latin America and then a another to the U.S. Even then you can check out other destination in Latin America. For instance, maybe you would want to fly to a hub like Lima and then book another flight from Lima to the U.S.

But from the Rio Airport you can fly to:
American Airlines Miami, New York-JFK
Continental Airlines Houston-Intercontinental
Delta Air Lines Atlanta
United Airlines Washington-Dulles
US Airways Charlotte