It's the PEOPLE, stupid...
Tourists predominantly visit a foreign country in order to see the local landmarks, which, in the case of Greece, are: the ruins, the sea, the sun, and... that's it!
Now imagine that, in some mysterious way, Greeks disappeared from Greece during the summer. WOULD YOU STILL WANT TO VISIT AN EMPTY COUNTRY? Would it not give you the creeps? Would it not feel like "the Twilight Zone"?
So here's my point: it's the local PEOPLE that make the local buildings and sights worth visiting. This is especially true for Greece: greek culture and civilization are a direct product of greek people. And, since people continue to "produce" civilization every day, there is NO WAY on earth that you, as a traveller, can even begin to understand the local culture, without getting to know the local people who actually produce it.
So, GET TO KNOW THE LOCALS, discover their life stories, their crafts, their hopes and aspirations, the places they go, the things they do.
And then, try to "copy" some of that stuff yourself, during your greek holidays. Start "feeling and smelling" like a local greek, in order to immerse yourself into the authentic greek culture.
It'll probably be the ONLY thing that you will remember, after returning home.