I would assume that it's because of its architecture and/or reputation for education and culture, not because it's a "vacationland." When cities compare themselves to Athens, they're usually talking about culture, not climate.
I think it's the sunny and warm summertime as well as the fact that there is a beautiful archipelago on the Adriatic coastline quite nearby.
Dubrovnik was the vacationland for the rich and wealthy of Rome. The Roman Emperors kept "alternate palaces" there.
Pearl of the Adriatic" or "Thesaurum mundi".
No not really Athens is better!!!!