LAN and Aerolineas both fly there from BsAs Jorge Newbury (AEP). According to wikipedia, other than those two, there is no scheduled service. I flew there on LAN and it was a great flight (modern A319s). I'd recommend LAN, as they don't seem to have the problem that Aerolineas does with later afternoon flights being delayed so much.

IGR is a tiny airport and the drive to the park takes about 15-20 minutes in a rental. The town of Misiones is about 15-20 minutes further up the road. Very, very easy drive through the beautiful forest. I'll second the notion to stay on site at the Sheraton. You can the beat most of the morning park goers and have most of the falls to yourself in the early morning just after opening.