You've already been given good advice.
If the Falls is the only destination you'll be visiting between Buenos Aires and Rio, look at AEP/EZE - IGR flights and then IGU - GIG/SDU flights.
It is very easy to travel between Argentina and Brazil in this area. You must stop at Argentine immigration when you leave Argentina. If you travel by bus will have to get off the bus and clear immigration, sometimes the bus won't wait and you will have to wait until the next bus comes along. Many people enter/exit Brazil without stopping at immigration - I don't advise you to bypass immigration. I choose to use a taxi for a trip from Foz du Iguacu to Puerto Iguazu last year and made the taxi stop briefly at Brazil immigration when I left; the cost was 45 reals. It is very easy to stay on one side of the falls and get a taxi to the airport on the other side, in your case if you stay on the Argentine side it's easy to get transport to IGU airport from there. Just allow time for immigration formalities at the border.