A search of this thread reveals that the RCC does not have shower facilities. It does appear that Air France has a club with a shower facility, which will be closed when I arrive this Thursday am on AA.

I will arrive at EZE at 10 am and need to leave at 4pm out of Aeroparque for Cordoba. Do you seasoned Bs.As. travelers have a suggestion for a place to go to shower that is convenient to EZE? I want to make one short visit in the city for a lunch meeting, but I need to leave that afternoon. It does not appear that there are too many hotels close to EZE that would fit the bill.