In this area of the continent, you will always have three options for everything, including hosting. Typically, people get used to staying in Foz de Iguaçu (Brazil). However, staying in other cities can bring you a small economic benefit because of the money currencies of each country.
I did couchsurfing in Puerto Iguazu (Argentina) for a weekend, then I traveled to Paraguay (read more about my trip in Paraguay soon) and, as my flight back home was departing from the Brazilian side I did couchsurfing two nights in Cidade del Este (Paraguay) and spent my last night in a hostel in Foz de Iguaçu.
As you can see, you can be flexible when it comes to seek accommodation in the three borders. Surely if you stay at the Argentinian or Paraguayan side, you may have to cross more times by the immigration. But everything is a matter of organizing and planning the visits in each country so you won’t have to cross again and again by it.
If you choose to stay in the Argentine side I recommend you looking for Marcopolo Inn Iguazu hostel in front of the bus terminal, very close to downtown. In addition, it is part of the Hi Hostelling International network, which as I have mentioned in other posts, usually have good discounts for members.
If you decide to stay in the Brazilian side my recommendation is to seek for Hostel Poesia. It is the coolest hostel I’ve ever stayed in my entire life. It was created by a traveler and his group of friends, to receive with comfort the tourists. You will notice that every detail within it is thought very carefully to give you a perfect experience. Comfort and Brazilian culture are pillars of this charming place. You need to know this hostel, and the helpful staff that works there, on you pass by Foz.
In the same street of the hostel are buses that take you to the terminal in the center. (Read here how to get around the three borders).
No matter which side you decide to stay in the three borders, you can be sure you’ll find cool people to enjoy your trip, have a chat, a beer and enjoy much of each country. Don’t be intimidated by the immigration process, the currencies of each country or by transportation, because in this region, everything is interconnected to make life easier for residents and visitors.