Here are my 2 cents worth (certainly not an expert!):
Akropolis M.: Fantastic building with amazing views all around. Contents are rather "limited"
National Archeological M.: Run down building but really amazing contents ranging from neolithic to hellenistic via Mycaenaic through classics. Simply great!
Benaki M.: "Esoteric"! Greek, Eastern, Ottoman, super collection...
Cycladic Art M.: (very close to the previous and the next ones). Very specific, stuff you won't see anywhere else in the world.
Byzantine M.: Unique collection of late Roman to Byzantine art.
All of the above reachable by metro, when coming from the airport you'd have to change at Syntagma to reach the first two, on opposite directions, though. There are several more small museums in Athens, let's leave it here.