From Athens International Airport “El. Venizelos”:

By metro/subway
Upon landing at the Athens airport follow the signs taking you to the metro station. Use Line 3 (Blue Line) with direction to "Dimotiko Theatro". You disembark at "Monastiraki" Station and pick up Ifestou str., in the end of Ifestou str. turn right and immediately left. We are the first building on your left hand side. Distance from metro station is approx. 300m.
The metro runs daily from 06:00 to 23:30.
Total trip is approximately 1 hour. Ticket cost 9€.

By bus
Just out of the airport's gate, there is a 24-hour bus service X95to Syntagma square, Athens, every 20 minutes. As soon as you reach Syntagma, you can use the metro/subway Line 3 (Blue Line) with direction to "Dimotiko Theatro". You disembark on the next station, "Monastiraki" Station, and pick up Ifestou str., in the end of Irestou str. turn right and immediately left. We are the first building on your left hand side. Distance from metro station is approx. 300m.
Total trip is approximately 1 hour. Bus ticket cost 5,5€.

By taxi
The taxi queue is just out of the airport's gate.
Total trip is approximately 40 minutes (depending on traffic). 

From Piraeus Port:

By metro/subway
The station is located out of Gate 5. You pick the subway on "Pireaus" station either with direction to Airport (Blue Line) or Kifisia (Green Line). On either line, you disembark at "Monastiraki" Station and pick up Ifestou str., in the end of Ifestou str. turn right and immediately left. We are the first building on your left hand side. Distance from metro station is approx. 300m. The metro runs daily from 06:00 a.m. to 23:30 p.m.
Total trip is approximately 1 hour. Ticket cost 1,20€.

By taxi
There are taxi queues in every gate of the port.
Total trip is 20 - 30 minutes (depending on traffic). 

Parking

There are a few private parking lots in the area. Unfortunately, reservation is not possible.