I can vouch for the Sunshine. They are on a side road from the main resort road so are less prone to noise from the bars, although not immune from noise from the odd late reveller returning to their room (but where isn't!). The accomodation is used by both British and Dutch operators.
It has its own Restaurant which can be exposed to a Sea Breeze but on a warm night you can dine happily under the stars. It also has its own pool and is run by a very welcoming Greek family.
The side road it is on eventually t runs past some larger all inclusive accomodation used by Germans before turning into a short dirt track that takes you to the Alikes (Greek for Salt Marsh) end of Tingaki Beach where there are sunbeds on the main beach. I would say that it is about a 10 minute walk if that. This takes you to the edge of the main sunbedded part of the beach. There are various paths in the area that will take you around the Salt Marshes (beware of Mosquitos) and one dirt track which will take you up to the main dunes between Tingaki and Marmari which is the Naturist section.
If you like Beaches but don't like noisy children on them, then the stretch of Beach between the sunbeds and before the Naturist parts really properly start are usually peaceful (except as happened to us when the Greek Airforce decided to give us and nearby Turkey a show!). Of course if you are feeling adventurous the half hour or so walk along the beach to Marmaris is enjoyable.
We have been in both May and October and weatherwise there is not a lot to chose between these months. I would imagine that in the high summer it would be too hot and you would have to resort to the more busier sunbeds.