Although expensive. Your best bet is to stay at the Sofitel at the airport. It's less than 5 minute walk to and from the terminal
I recommend the neighborhood Markopoulo which is next to the airport. (Message me for an Airbnb recommendation). Someone told me that they had Ubered there for 6 or 8 Euro. It is a walkable little town. The apartment where we stayed had a nice little square with restaurants, cafes, grocery, bakery, etc. Very easy and cute! We stayed there arriving and departing Athens when we had to return the rental car at 6 am at the airport. I think you are two exits away from the airport at Markopoulo.