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The old "original"part of Athens for sure, "Plaka". Both the pre 20th century town and the ancient artefacts in/near (ncluding the Acropolis[/size]

) it are perfect for your shoot.

 
plaka athens

 

Lykavittos Hill gives a great 360 degree view of Athens, which may give nice backdrops both day and night.

 
https://b.geolocation.ws/img/030/032/103-F.jpg 

Acropolis, with the Parthenon, in front, with Lykavittos Hill in the background.

 

Can't recommend on islands, as I have no idea about the time you have available and ferry schedules and durations.

Thanks soooooooooooooo much!!!!