We will have 4 full days in Athens during the last week of June. I have three days of seeing sites and shopping with an evening trip one of those days to Temple of Poseidon. The 4th day I am leaving open, but curious of fun, more relaxing things we could have as options. We do not want to do a lengthy day trip out of town, although not opposed to leaving Athens, just nothing with a several hour drive as we fly back to the US the following day. Any thoughts?
Is the Kolonaki neighborhood on your itinerary? Check out the Cycladic Museum,and Benaki Museum.
Some ideas if you want to get out of the city center of Athens without going too far:
Have you heard about the SNFCC? (Stavros Niarchos Foundation Cultural Center) I like to go there to get some fresh air in a nice environment. There is a large park, exhibitions, entertainment, an impressive library, a few places to have a drink, including a lounge bar at the top with relaxing music and a 360° view of Athens and the sea
There are free shuttles from the city center to get there.
And it's not far from the Piraeus marina with its rows of wealthy people's yachts that can be the subject of a stroll
https://maps.app.goo.gl/3zR9CiFDTanDUPTv8
Or, at the medieval Kaisariani Monastery you will also be in the countryside in the middle of a park, although only a few kilometers from the city center. As a bonus, a splendid view of Athens. Unfortunately there is no public transport to get there, take a taxi.
Have you considered a beach club, if the weather’s nice? We had nothing planned for our last day in Athens and saw the hotel was offering free transportation to a beach club down the coast so we went. We had planned to take the tram back early but it was so much fun we wound up staying all day! Good luck with the trip!