Museums are open longer in the summer than in the winter; usually until 8 PM or dusk. In the winter they tend to close around three as do out door sites.
Museums are often free on Sundays and closed on Mondays. But others like the Benaki Museum in Athens are open on Mondays and closed on Tuesdays so calling them in advance to make sure is a good idea!
Greek officials love their rules (left from Delos Museum) and as you'll see below if they can make them complicated then so much the better!
So I have chosen a few of the most popular spots to give you an idea of the hours and fees!
Using your flash is frowned upon in Greek Museums for some reason. I think that after laying around in the mud, snow, rain, ice, hale and wind for over a thousand years the marble will survive your flash, but apparently I am mistaken. Never argue with a Greek bureaucrat! They let dogs run around outdoor sites freely peeing on stuff and worse but paying customers in museums are not allowed take flash pictures and forget about restrooms. The reason they wont let you take flash pictures is that if they let everybody take flash pictures then they couldn't charge professional photographers and authors money. I have seen 'allowed shoots' in my museum visits complete with klieg lights and more and no one was worried about the effect of the bright light then!
Here is an example of the Days of Admission and days of Free Admission for all visitors of the National Archeology Museum in Athens which is the most important museum in Greece: Telephone: 210-8217717, 210-8217724