What should I take in the way of a jacket? Will a windbreaker do? Might I want something warmer at night? I will be there essentially the whole month, including the islands, Olympia,, Delphi, Meteora.

I would think you could layer in the evening if you needed to. I can't imagine needing anything heavier than a windbreaker. We've gone to Greece twice in May an both trips had beautiful weather.

I've been there in May when it was cold, windy and raining steadily for a week, although that's not normal. My point is that you can't predict the weather. Bring a light jacket or sweater. Hopefully it won't leave the bottom of your bag.

Yes you will definitely need a jacket, especially in places like Delphi and Meteora where it can get cold at night. Durning the day it will be warm, but there might be a few less warmer days too.....
Right now Athens has 19 -22 C daily ....

I think the windbreaker should be fine, it was enough for me in Halkidiki in early May. But it depends how each person is feeling the heat or the cold.

My experience in May is: windbreaker PLUS liteweight cotton Cardigan. Late in May, all u will need after sunset is cardigan over shoulders. In Early may if it's a windy day (or sudden short cloudburst), or if u are on a ferry & it's cloudy/windy -- you'll welcome having both. To ease packing WEAR them both onto the plane from US.

During the nights it is most likely to need a jacket, not a very warm one, but a normal

Yes, a jacket would be helpful in May. During the day, the Weather will be softly warm, and during the night a bit cool, especially in places like Delphi, which is located on a Mountain.