Ezeiza: the main place to spot is a staff canteen located on the control tower building, right above the Aerolineas Argentinas terminal. You walk out of AR terminal to your right on the direction of Terminal B (the one were most international airlines operate) and around the corner is the entrance of the building. Take the elevator to the 3rd floor and there is the cafeteria. The place is not great but the only available at the moment; you can have a general view of the tarmac and the taxiway were most airliners pass when departing, also the runways behind. Stained windows, except two but with a good zoom should be no problem.
Another place to spot (not good for photography and discouraged as there is some police around) is by leaving the Aerolineas terminal in the arrivals area but to your left. Walk on the direction of the cargo offices. You will reach a control door with police which is located behind gate 13 so you are close to the aircraft parked (in general Aerolineas B747, A340 or Iberia) there and can see some behind.
A new terminal at EZE is going to be open in June, with lots of glass so that will be a new spotting area in the future.
Enjoy your trip,