Although it is very early (maybe the following information will not be valid
until October, because the extension of the Metro at the middle September),
I send you the current status:
>From the West Airport there is the bus No B2 which goes to Panepistimiou str. and has a stop at Amalias str, very close to Syntagma Square and to hotel Amalia.
To go to the Airport there is another stop of the same bus, also in Amalias str, so you don't have to walk very far with the luggage. The only problem I can see is that the bus above is a regular bus (not express) and does many stops. So you need to count to your schedule the time you need to go to the airport (I think more than 1 hour while traffic).
In case your flight arrives at East (International) Airport, there is another bus (No 091) which goes close to Omonoia Square, by passing through Syntagma.
Note that all the above maybe will not be accurate until your trip. You can contact me directly some weeks before leaving for verification. I hope I have helped you. Best Regards from Athens Joanna