What a great question!
To me, this can be explored from different points of view, but it always comes back to the idea of a sense of continuity with the original myth.
As a person born and educated in the Italian school system, the classics crossed my path many times since I was a little child, not only in their original form, but also through their many retellings.
I think it is a constant leitmotif in our literature trying to find new ways to extract modern reflections from ancient stories.
For this reason- I always tried to start from these ancient stories, or at least their tropes, to tackle themes that, in a very Italian way, talks to our modern readers.
In my perception, Ancient Greece especially means Philosophy and -nowadays -the most tangible expression of philosophy is -of course- Ethics.
So, to me, an island to be Mediterranean in a modern but authentic way, has to be rooted in ethical enquiry.
On the other hand, landscapes are a crucial way to frame a Mediterranean place. Even deciding to describe an unusual scenario, I tried to research a bit about endemic species, typical rock structures and prevalent colors, so that every island I depicted is somehow derived from the description of a real island, and then twisted a bit.