Not a lot of choice in Athens itself: The Zea marina and Kalamaki are typically both very crowded, noisy and dirty. You should try more eastwards in Olympic marina just south of Lavrion. This IMHO have a better service, normally have space and it is actually the marina closest to the new Athens airport.
If you luck out, there is unfortunately not a lot of more options as good Greek marinas are like gold dust. You have to either go west into the Ionian and try the Levkas/Preveza area and north to Corfu (Gouvia). Or you have to go east to Turkey to find a good marina. Not a lot in between. Great beautiful harbours for anchoring, but not a lot of places to leave your boat safely in.
Edit note: let me mention this before someone tries to score a point here; there is actually a very good Greek marina on the island of Kos. However, once you get this far east you are 8 nautical miles away from the Turkish town of Bodrum. There are three world 'Gold Standard' marinas in Turkey within 10 nm's of Kos so you have a great choice once you get this far east.