This is how to experience the real Greece. If all you want is a photograph, then join the mobs of tourists in Santorini. But if you want to experience the warmth and beauty of the Greek people, the food, the culture, then stay with Kostas and Maria in Kynidaros. They are salt of the earth, amazing people who make you feel like a long lost relative. You may find yourself at their table drinking homemade Raki, making Greek salad with fresh vegetables from their garden, and learning so much about traditional life in a small Naxos mountain village. Drink coffee on the balcony and take in a gorgeous country view that goes all the way down to the sea.
Naxos is a wonderful choice of Greek isle and you can access it all from Kynidaros. If you have a car or scooter, great. But you can also get around with a combination of buses and taxi. You can enjoy the mountain tranquility of Kynidaros and still explore the offerings of Chora and the beautiful beaches. We were able to do it all. And with the money you save staying in the village, you can stay longer and really relax and settle into the slower pace of life.
If you want to get to know the real Greece, Kostas and Maria and their family are more than happy to show you. I highly recommend staying at their AirBnB.