We loved Maganari Moments, a peaceful oasis where you can recharge. A 40 minutes drive from Chora, it is perfect if your holiday is beach-visiting-oriented.
With a little organization you can easily overcome the "problem" of the distance from the center/markets/groceries. The breakfast as well as the aperitif on the terrace with an amazing seaview have no price.
The car rent is highly suggested.