Hey WHOA - on May 1, Labor Day (everywhere in the world except USA!) is the holiday when NO public transport runs ... so you will need to take private transport (taxi) on arrival. There is no Uber alternative; Greek govt. banned Uber last week, unless there is a change before May. Since there will be a HUGE demand for taxis, You would be prudent to use a car service. Be aware that rates can vary widely, & why pay more? A recent RS thread recommended this one that charges same flat rate as taxi!
"used Welcome Pickups in Athens last year. Excellent service, met at arrivals, driver spoke excellent English, welcome bottle of cold water, beautifully clean and new car (and drivers don’t smoke in the car!) and delivered right to my hotel in Plaka. Also used them to return to airport at end of trip; cost was €38 each way paid in advance before I left home."
Something to keep in mind when returning to Airport before dawn:
Taxi flat rates are Day €38 from 6 am - 12 midnight, night rate about 60+% more, from midnight - 6. I believe the rate is charged by the time you ARRIVE at a destination. If you had a taxi pick-up at 5:30 am, you probably would arrive at 6:15 am & get the day rate. The X95 Bus at Syntagma (€6; €3 seniors) runs 24/7. If you are 20 minutes away, and are in a good neighborhood (NOT near Omonium) you can very well walk to it. Staying around the SOUTH side of Acropolis (by the pedestrianized walkway), I have done it pre-dawn, rolling my luggage up Amalias Avenue, the very busy 6-lane thoroughfare at eastern border of Plaka. Even at 4 am, there was steady traffic, and people leaving clubs (athenians are Night Owls!).