You are still wasting too much time in transit for such a very short stay in Greece ... 2x in Athen area, also, doing a FERRY to Naxos taking most of a day ++ (when u count checking out of hotel 6a m, getting to Piraeus, boarding ferry /sailing from 7:30AM- 12:45, disembarking/getting to hotel, checkin in =7.5 hours!!) ... also Athens is a busy bustling city just like rome, will you feel energized to plunge into sightseeing after checking in to hotel at 3 pm May 21, going to Acropolis etc etc? I wonder. Doing islands first is a much better intro to a country, have your 1st sunset overlooking the sea ... slower pace, get used to Greek ways, revitalize, be ready for Athens at the end (also... after being immersed in Greek history etc for a few days, Athens landmarks & treasures resonate MUCH more. Believe me, from experience, traveling with newcomers during 9 of my 12 trips).
My suggestion:
• May 21 arrive noonish, take Aegean flight 15:15 (3:15 - 3:55) To SANTORINI -- you're in luck!! it's €86+, GRAB IT!! Many hotels pick u up at airport, plenty of time to check in, maybe have a quick dip (if yur budget stretches to a pool hotel) and find a nice restaurant for drinkies, food & view of sunset, it's not until 8:45 or so (NOTE: do NOT subject yourself to sunset in OIA, it's a zoo -- we can recommend many wonderful spots to sip and gaze serenely, elsewhere).
• MAY 22 - 23 -- Santorini
• May 24 - 10:45 AM take CHAMPION Fast-ferry (rear deck allows lovely departure view) arr NAXOS by noon!
• MAY 24 Afternoon + May 25 - 26 - 27 - Naxos.... swim, hike, drive or bus thru dramatic landscapes, explore port town etc
• MAY 28- 10:25 Flight NAX - ATH arr 11:10 (€80-- but its 45mins vs 6 hours ferry!! dont wait - these smaller planes fill up FAST) - Taxi to Central area hotel check in by 12:30, ready to explore Athens!
• MAY 29 - 30 -- Athens landmarks, museums, food, nightlife
• MAY 31 -- Flight home