So after some changes to our upcoming trip to Greece, we will be in Athens later in May, including Sunday May 18 International Museum Day when the museums and archeological sites will be free admission. We will have a full Sunday, Monday and Tuesday in Athens and I am choosing one or at most two main sites to visit on that Sunday and then fill in with neighborhood wandering or smaller sites.

Which do you think would have the smaller crowds on a free day?
Acropolis (I would expect it to be the busiest)
Acropolis museum
National Archeological Museum
Ancient Agora

I assume the changing of the guard attracts a larger crowd on Sundays with the more elaborate ceremony.

Thanks for your experience with free days at Athens sites.

I have no experience with International Museum Day in Athens, so forgive me if my comments aren't quite on target! I think you are most likely correct that the Acropolis will be most crowded. My bet is that the Acropolis Museum will also be mobbed. FWIW, I thought the National Archeological Museum absolutely magnificent and well worth most of a day, and my impression is that it doesn't get the same crowds on any day as the other museums you list. And it's HUGE, so if one section does get crowded, you can easily move to another section.

Have you seen my TR? It might provide some useful information, as I visited all the museums you list ... and many others, too. The section on Athens begins with post # 181:
With Gratitude for a Glorious Solo Month in Greece

BTW, my experience with International Museum Day in other locations is that some museums are open later ithan they might otherwise be. I've been glad to take advantage of those late hours, so you might want to explore those options, too!

I do not have experience either with free museum day in Athens, but from my experience visiting there, Agora does not get that crowded in general (the other three are usually packed). We got there at opening, only a handful of people. When we left, a couple of hours later, there was a line, but not that long. If you go there, download the free Rick Steve's tour of Agora. It was great, easy to follow and informative.

We did experience free museum day while in Nafplion, and visited some archeology sites free. The crowds were not bad at all. In general, sites that tend to get the bigger crowds we usually aim to get there at opening, to beat the tours.

When we went to the Agora first thing, we had the place to ourselves. Where was everyone? At the Acropolis.

There are TWO agorae in Athens -- the Roman Agora and the Ancient Agora. In late May of 2019, I visited the Roman Agora in (I believe) the late morning; there were other people there, but not too many. I believe I visited the Ancient Agora in mid-morning; again, there were others there, not too many, though the numbers were increasing.

The Greek Agora is the much lager site, about 30 acres and includes the Temple of Hephestus, the most intact Ancient Greek temple, as well as the Stoa with its own impressive museum. Visitors usually get spread out.

The Roman Forum (that is how it is sometimes marked on maps) is no mare then one-fifth the size and can be viewed from the gated perimeter without entering the site. I found it rewarding to enter, though many people just walk by and figure there's not much else to see. Because of that, it does not get crowded despite heavy tourism.