I'd go for a day rate at a relatively inexpensive hotel to use as a place to drop bags and shower, ideally in a neighborhood where you want to walk to sightsee so that you can return easily to relax whenever you want. You do not want to risk being forced to spend hours landside at EZE and even hopping between several lounges (there's also an AmEx Centurion lounge in the SkyTeam area of the EZE airside terminal) would be a very boring and frustrating way to spend a day.