I've noticed a variety of family-friendly type restaurants at EZE, but I've never considered eating there so I don't know. You should probably check out the lounge food first to see whether the free stuff is enough. Would a big late lunch work on your last day in BsAs?

Yes you will have access to the AR (departure) lounge at EZE as a SkyTeam ElitePlus (DM/PM/GM) traveling on a SkyTeam international itinerary. [You can verify this on the DL website using the lounge access drop down menu as well as on the SkyTeam website.] The lounge is clearly AR operated and not a contract lounge, so you should have access even on a basic economy ticket. IIRC I've just shown my boarding pass and passport to enter; I don't think you need a lounge invitation, but it might be good to ask at the check in counter just in case.

BTW, unless you're traveling during Christmas high season, I would think that a PM would have a good chance of a C+ "upgrade" (if you want it---watch out for being "upgraded" to a middle seat with more legroom) on the DL EZE flights as they don't seem to be elite heavy and often have lots of nonrevs in D1 and C+; I've also seem a lot of OPUPs as coach is often full. In that case, you would be served first and surely get your meal choice, so eating on board might not be bad. IME the FAs on these routes tend to get meals out quickly, but my experience is in business class and not around this time of year.