The Melia Iguazu (former Sheraton) is the hotel inside the Argentine side of the park.
The Belmond Hotel das Cataratas is the hotel inside the Brazilian side of the park.
There are plenty of hotels.resorts.pousadas/hostels in Foz do Iguacu and Puerto Iguazu, in the towns and closer to the park entrances and airports.
The last poster with a question is taking a day trip though.
Thrilled you edited your post for correct English (boarder vs. border). Now it all makes sense.