Iguaçu is the part of the falls in Brasil - perhaps 20%. Iguazú is the Argentine portion, the vast majority. The Sheraton is the place to stay - as soon as the park opens you are there, and you will not have to pay two days' entry fees (only when you arrive to proceed to the hotel.) There is splendid walking and wonderful views - start early and you will see flocks of parrots, some toucans, monkeys... but by the time the tour busses arrive and take the train into the park, they will start to fade away; they do begin to come back just before the park closes, and the Sheraton is at the park margin - much closer than the entry block.

I'm with KSinNYC on this one - we spent three nights, and enjoyed the walks, the forest, etc. etc. and one day in Brasil (they may wave the $100 reciprocity fee for a visa if you are just spending the day at the Brazilian side of the falls - the falls, the bird park and perhaps the helicopter ride are the things to do, and watch for the aggressive coatimundis - they will bite you and slash your backpack if they detect food on you or in your things. The trick is to visit Iguazú weekdays, and avoid the crowds on the weekends and holidays.

Patagonia is huge - and we don't know what you like. The more spectacular mountain areas include the Perito Moreno glacier... but another interesting place to consider is Punta Tombo with its enormous penguin colonies, orca whales, rheas and guanacos, etc. Again it depends on what you like - Argentina also has spectacular wine country, and some could easily spend a week in Bs. As. sightseeing and doing day trips to Tigre, to nearby Colonia del Sacramento in Uruguay, the trip to Iguazú, a gaucho celebration at a nearby finca with its attendant dancing, gobs of open-fire cooked meat, etc.

IMO investing in a book or two would give you some good ideas, and allow you to express your preferences - we will definitely express ours!