As a source of ideas, why not take a look at a map of all the European destinations served by direct flights from Athens?:
http://www.aia.gr/flight_schedule/european_en. htm
(Place your cursor over each destination to see which airlines serve it).
I can't see that there are many suitable non-European destinations but, for reference, here's the map:
http://www.aia.gr/flight_schedule/default_en.h tm
The most obvious choices (i.e. destinations which are usually considered 'romantic') would seem to be Paris (possibly not guaranteed to be sunny enough), Venice and Rome. However, I'd suggest taking a look at the possibility of Barcelona. It's a city which has something for all tastes. (Great beaches, both quiet & lively bars, fantastic restaurants and loads of history & culture):
http://www.barcelonaturisme.com/?go=jN7uAYLx/o IJaWVQCb4ZU93ygJVYLOpRQdvyIue/wAW6Ddhyhal0Y8Jy bdczumN4RSbo3CRL94sJBt7u1Kc=
Chris