Wow! What difficult question! I can't comment the Rio option as I have never been ( for some reason it has never appealed to me).

Peru - this is a well trodden circuit and travel is relative easy and good value.. I loved all of the places on your list except that we didn't make it to Colca. Depending on the time available, I would include Titicaca which is easily accessed from Cusco via the Inka Express. There is also a regular bus service to Arequipa. For hiking, I would recommend the 3 day trip from Lares to Ollantaytambo.

Argentina - Iguazu is, of course amazing and Salta and the NW is one of my favourite places in the world but you do really need a car to make the most of it. An alternative would be to hire a driver and guide. Angie Valdez (aka Flintstones who posts here) would be worth contacting. We got the bus from salta to Iguazu which was a long trip of some 20 hours but was very comfortable and was scheduled overnight thus reducing the boredom factor somewhat and saving on accommodation costs. Ejecutivo or first class was around 25_30% of the airfare and was similar to a first class cabin on a decent airline. The sights of the northwest were spectacular but not too sure about the hiking options. I am sure they are but we just didn't look for them.

It is a really difficult choice and as we are returning to SA next year, we are facing a similar dilemma, in our case whether to include Columbia or Bolivia. Peru and Ecuador are firmly on the list and, if we do go to Bolivia, it is a short hop across the border to Salta.

A few photos and more detail of our time in SA. It is four years old now but I don't suppose it has changed that much.

Entries #55 on cover South America http://blog.travelpod.com/travel-blog/candcthai/1/tpod.html

Thanks for the reply. I like your pics.

I will probably end up doing Peru. Buenos Aires and Iguazu will still be there in a year or two.

If you are using your AA voucher, ask if they can include Cusco (either open jaw or with a stopover in Lima). The Lima to Cusco airfare is an expensive domestic ticket to buy independently.

May is the beginning of the dry season in the Andes, a very good time to visit since it is still green, not much rain, but not yet high season.

If you do this with a stopover in Lima, you can roundtrip to Huaraz/Cordillera Blanca, or to Huancayo (the train runs in May).

I did the train this year

http://www.fodors.com/community/south-america/the-high-altitude-train-to-huancayo.cfm

Thanks for the recommendation. You said the train runs irregularly. Do you know the schedule?