Originally Posted by
Xandrios
I would add that the bus at that time is probably actually faster and easier than Metro anyway. And a few bucks cheaper too.
Bus:
http://www.oasa.gr/xmap.php?id=px95
Click on "backward direction". You will start at KTIRIO AFIXEON (=arrivals) and go down till AFETIRIA (=bus starting point, being Syntagma square).
Regarding luggage: If you arrive at 4AM that sounds like the either the Aegean or BA flight from London. In case of BA I would suspect that the flight to JTR is on a separate ticket. If that is the case then you may need to retrieve and check your luggage again. Which probably will not be possible so early. If you are on one single ticket it should be no problem to check your luggage through to JTR from your starting point.
We had a similar layover although we arrived a couple of hours later...We left our luggage in a locker at the A3 club (don't know what time it opens). Since you're *A gold, you have access. Then we took the metro into the city to Syntagma square and walked to the Acropolis...it's one of those icons that just should be on everyone's bucket list...then walked to the Acropolis Museum which was great and where we had a very nice late lunch in their dining room with a fantastic view of the Acropolis and Parthenon.