I did a similar trip, Rio to Santiago, although I took a bit longer. You may find my TR helpful: Rio to Santiago via Patagonia

I would probably head from Rio up to Igauzu and cross the border there. Spend a few days at the falls and then head to Salta in NW Argentina. The best way to see the the NW is to rent a car and drive two circuits of the regions startining in Salta city. 7-10 days would be perfect but you could do either the north or south circuits in less time. Some detailed info and photos etc on our blog @ https://accidentalnomads.com/categor...ica/argentina/

To get down to TDP you could either fly via BA or go via Mendoza, Bariloche etc or down through Chile (Pucon Etc ).

we have generally travelled trough Argentina by overnight bus rather than flying. A surprisingly comfortable and efficient way to travel, especially given the reliability of airlines in South America

We went from Santiago to Mendoza by bus and it was incredibly comfortable - I commented that all the airlines could learn a lesson or two from the bus companies!