If you're coming to Athens in May, check the "This is Athens City Festival" event schedule:
https://cityfestival.thisisathens.org/en/
Some free live Greek Folklore events as part of this festival that might interest you (all the details in the links).
May 4th at Mitropoleos Square: Wedding Songs-Music-Dances
https://cityfestival.thisisathens.org/en/event/wedding-songs-music-dances-from-thrace/
May 17th at the National Garden: Lykeion ton Ellinidon
https://cityfestival.thisisathens.org/en/event/lykeion-ton-ellinidon/
May 30th at Kotzia Square: Evritiki Zygia
https://cityfestival.thisisathens.org/en/event/thracian-panigyri/