Nothing particularly interesting nearby in Brazil, other than maybe the Pantanal which you don't have long enough for.
Aren't there the San Ignacio Mission ruins in Argentina? Fairly nearby.

Are you sure that's too long? I'm spending three nights at Iguassu, and you could surely find something to do in BsAs.

Although most people only spend a couple of days, I wouldn't say 3.5 days is too much. We were there for 4 days and spent a day each in both the Brazilian and Argentine sides each providing a different perspective. The Braziilian side is more panoramic, whereas the Argentine side allows you to get up very close to the falls and take boat rides etc. you could easily spend the whole day around the argentine falls.

Foz de Iguazu town is quite pleasant and worth a few hours and it is easy to get through the border by bus but you should be aware that if you do it "officially" and check in at the border, the fees are high for some nationalities, notably Australian and American.

We did not go on any jungle or river treks whilst there but Marco Polo hostel, where we stayed, had many optiions on offer apart from the usual trips to the falls. I am sure you would find something if you googled.

Alternatively, just take the standard 2 day trip and spend an extra night in BA which will eat up your time as there is a lot to see.

A friend and I visited San Ignacio Mini Reducciones last January, as part of the Iguazu side trip from a BsAs/Santiago vacation. I enjoyed this change of pace, both the ruins and the interesting people watching on the bus ride through the campo. My friend crabbed about the effort it took to see "a pile of rubble" in the blazing heat. (Other than that, we got along famously!)

We did not take an official excursion. It's possible that the trip from Puerto Iguazu to the ruins would be quicker that way---but I didn't mind spending my time on the bus.

Another option is Colonia. I have checked the ferry times but I would think you could do it as a day trip.

A nice day trip (or an overnight trip) from Buenos Aires is to visit an estancia. Several years ago, we visited Estancia El Ombú, near San Antonio de Areco (which is worth a look too.). http://www.estanciaelombu.com/eombu.htm

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Vic's travels: http://my.flightmemory.com/vogilvie

Iguazu: In addition to seeing the falls from both sides, Iguazu Forest Eco-adventures offers a spectacular excursion that includes rappelling down the side of a waterfall and a zip lining over the tree tops. I have been on this excursion several times and each year they have added to the length of the zip line....

Buenos Aires: I am unclear whether the BA portion of your trip is the only time you will have in Buenos Aires or whether your organized tour will include tours of the city. Assuming you will see BA via your pre planned tour and you are looking for additional activities outside the area, a day trip to the Delta is well worth your time.....this tour company come highly recommended and includes several pages of photos of this unique area.
http://www.delta-unplugged.com.ar/index-en.html

If you like horseback riding and want to get out of the city for a day, I highly recommend this estancia.

http://www.estancialosdoshermanos.com/index2.html

Here is the link for Iguazu Forest. I forgot to include it in my previous post.