I'm looking at a flight that would land at ATH at 16:45. Then probably arrive in the city after baggage claim around 18:00.

I've found Cosmote and Germanos stores on Google Maps, near Syntagma Square.

But are they open past 6 PM?

The plan is to go to Mykonos the next day, so there may not be an opportunity to go to the store before. I know the ferries depart very early. I may take a flight but I'm not sure yet.

They apparently have stores on the islands but I'm wondering if it wouldn't be a better idea to get a prepaid SIM in Athens.

I was surprised when I looked at the Cosmos website that it showed store closing hours of 15:00. Not sure about Germanos closing hours, maybe they stay open later.

I no longer bother buying SIMs for my phone when I go to Greece unless I plan to make a lot of local calls. There are wifi hotspots everywhere these days, so it's easy to get online and make Skype calls without a SIM. I just leave my iPhone in airplane mode and turn wifi back on in Settings.

Unless you have an urgent need to use the phone right away, I would use the evening in Athens looking around the city and finding somewhere for a nice dinner. If you do decide to fly to Mykonos, you can stop at the Germanos store in the airport domestic departures area.

I've never used the Germanos branch at Mykonos, but their island stores I have used are quite good. I even found a charger for my iPad at the Paros branch last September when the one I brought with me failed.

Autocorrect fail! Of course I meant Cosmote rather than Cosmos.