Athens Airport Taxis are available at the designated Taxi waiting area located at Exit 3 of Arrivals Level. The queue during high season starts outside exit door 2. There are lots of taxis so the queue goes down really quickly.
Yellow taxi prices vary depending upon the time of day, the number of passengers and the season. There is a fixed rate as seen on the board at the head of the queue which covers quite a large area of central Athens from AIA for a fixed price. As the port is not within that area, based on 2016 prices you should budget for at least 50 euros to get you to the port at Piraeus for your onward journey to Hydra. Confirm the price with the driver before you leave.
Make sure that the meter is switched on and shows tariff 1 (tariff 2 applies after midnight and is twice as expensive).