Access to Zappeion is very easy by public transport.
It is located at a walking distance from Syntagma metro station, the tram, yet also many buses and streetcars connecting all areas of Athens.
For more information, you may browse the following sites:
From the airport:
From the airport, you may use the Metro (about 50min to Syntagma) as well as Airport Express Bus Χ95.
From the port of Piraeus:
From the port of Piraeus, you may use the electric railway and the Metro (about 30min).
Zappeion does not have a parking space.
You must leave your car at nearby parking stations around the area. www.parkaround.