A couple years ago we chose Greece as our annual run away. Instead of focusing on the main land, however, we went to the islands. We spent a few days in Rhodes, several more in Karpathos where we visited a family friend with a home on the island. There we were able to get familiar with the community, visit in some homes, and go to some traditional village feasts, and events. I found the people to resemble my family more than any place we had ever been, though we have no known geneology connection.
This island is not a night pot or tourist laden place, but it is perhaps one of the most authentic of the places.
On the way there we stayed at the Athens Marriott and from the top floor roof restaurant we found ourselves staring at the ancient acropolis.