AA doesn't fly there, you can fly AA to EZE stay some days there. Then fly Aerolineas or LAN. Iguazu and Calafate are opposite sites, both very interesting. If you go to Calafate go to see the Glaciar Perito Moreno and different glacier excursions. You can have a Chivas with glacier rocks sitting right there in the ice. Check for Bariloche and Villa la Angostura.
Please tell me if i can help you with anything else.