Although Villa Coralia is listed at VRBO but you can find this villa on other sites as well.
Certainly not in walking distance to beach but you may not want to leave. It sits high up on the hill and pretty sure it is private that no one else can see you
Check out sites as I have found that you can enter 4 guests and still have Villa to yourselves.
I have been doing much searching for next year and this has to be one of the most beautiful and reasonably priced.
The view is stunning.
We plan to to a visit this August while we are on island
Plan on hiring chef franc (formally owner / chef L'Estiminate) to cater a meal, also reasonable
We did find some on VRBO with pretty good views and directly behind beach bars.
They may be available indirectly and not just through VRBO

Best wishes on finding the right property