Suggestions for day of arrival in Athens?

I try to never do anything indoors on arrival day--sunlight helps with jet lag. I would do a walking tour (take your pick--lots of great neighborhoods) and try to see the Acropolis on that day, as you may catch a break with the line in early evening, then do the museum the next day when you are refreshed.

I would keep your plans light, you will be coming off a longer than normal travel day to Europe, no telling how you will feel.

Focus on free or low impact sights. Walking around usually is at the top of my list, spending time outdoors. Getting to know the Plaka area is good, maybe wander the Agora, you could see Syntagma Square, the guards at the monument to the Unknown, Wander through the National Gardens, see the Temple of Zeus, basically lots of things that require no prebooking, and are flexible depending on your energy, and maybe the weather.

The Orthodox Holy Week of Easter, the most important event of the year in Greece, will take place this year in the first week of May. And given that Holy Wednesday falls on May 1 st which is a mandatory public holiday (Labor Day) , the Greek Minister of Labor has decided to postpone this public holiday to Thursday, May 7.

The decision to move the holiday from May 1 to Easter Tuesday was taken in order not to disrupt economic activity at an important time for trade and consumers.

Therefore it is likely that all museums and archaeological sites will be closed on May 7 instead of May 1 st like other years.

To be confirmed in the coming weeks. To date, no specific information has yet been published by the museums and sites.

Also note that the vast majority of businesses will be closed on Easter Monday, May 6, 2024 (even in tourist areas)

We will be arriving after a short flight from Vienna so jet lag won’t be an issue. I do know about Labor Day being changed but unfortunately there isn’t anything I can do about that now so any suggestions of things to do that day would be great. The museum website does not list Easter Monday closed but does for Easter Sunday so that’s part of the reason I’m looking to make the most out of our arrival day.

There are so many things to do in Athens apart from seeing the archaeological sites and museums that I can only advise you to visit the city's official website:

https://www.thisisathens.org/

Go for example to Anafiotika neighborhood, it's a small part of the Plaka district and there is a Rick Steves video on Youtube.

https://www.youtube.com/watch?v=beiWL-80AVc&t=7s

We went up to the Acropolis in the afternoon. As it closed, the employees headed down the long stairway, with us just ahead of them. At the bottom of the stairway, the top of Mars Hill was still very much open. With good weather, you could visit the Acropolis, at not the busiest part of the day, and stay until closing, if you chose.

If we were to try to see the acropolis on the day of arrival I would be nervous to purchase a ticket ahead of time with a reserved time just in case our flight was delayed. Would it be possible do you think to go to the entrance by the museum and purchase our ticket for that day when we arrive?

Would it be possible do you think to go to the entrance by the museum
and purchase our ticket for that day when we arrive?

Of course, you can go to the ticket office and buy tickets without having pre-booked them. Since the Acropolis has not communicated specific opening times for Monday May 6, we can assume that you will be able to go there until 7 p.m.
Which could be a good option given that the main part of the crowd leaves (theoretically) around 5 p.m./6 p.m.

The South entrance located on the south-eastern side of the landmark, near the Acropolis Museum is (still theoretically) less busy.
it's here:

https://maps.app.goo.gl/hZSj2r7oCBfqaeVAA