I found 'Villa Achinos' (Stylish Seaside Villa for Two) last year. It is the perfect size for a couple with an excellent large garden with a salt pool and really comfortable sunbeds. So comfortable that we stayed at the villa quite a few days without moving. But a two minute walk takes you to the "donkey beach" where on a busy day there might be 2 or 3 other people sunbathing on the flat rocks.
It is less than 5 minutes into town in a car or a 20 minute pleasant stroll. The property is gated and is in a lovely quiet area. It is roughly equidistant between Gaios and Mongonissi. We rented bicycles for a few days and cycled to Carnayo Gold restaurant at Mongonissi and on another day we cycled (*pushed the bike up the hills) to Loggos which is a MUCH hillier part of the island.
There are a few houses along the road but you get privacy, with an occasional passerby along the roadside but the pool area is raised so no one can see much!
We loved it and have booked up to return this year. We have already recommended to friends who also enjoyed their stay last September.
Great stay in a lovely villa on a lovely island. Villa is modern and clean in a nice quiet location. Nearest shops and restaurants are about a 25 minute walk away so you may wish to hire a vehicle if you are not up for a walk each day. The owner was very helpful and organised transport to pick us up from the port and then again on leaving the villa