We went to Naxos in April with our two kids (4 and 2). We really fell in love with the island : it's very nice with beautiful mountains, with thousands of wild flowers in Spring, and it's very easy to do some hikes with the children. Damarionas is a nice small village at the bottom of the mountains, with a small shop where we can buy bread. The location is just perfect. There are also supermarkets in Filoti or Halki, 5 minutes drive from there. Damarionas people are very welcoming, our eldest boy even played with some kids from the village. It is safe as there are no cars in the village center.
About Polyvios house : We really want to thank Polyvios for his warm welcome and his help for the organization of our trip. He really did everything to make our journey the best, he even provided us toys for the kids. The house is confortable, perfectly clean, with everything you need inside.
We really recommand this place and we hope to come back one day!