I too prefer the peace, quiet and tranquility of not having too many kids buzzing around when I am relaxing in the van.
However, having tried quite a few Adults Only sites, I have not enjoyed them at all and now we don't even bother going to these sites or paying the crazy premium prices they all appear to charge!
We found them to be generally very poor value for money with high prices and small, cramped pitches. In addition, we found the campers on Adults Only sites to be stuffy and generally quite miserable... (I am not interested in chatting with every camper on site, nor do I go away to make new friends but common courtesy and a genuine "Good Morning" isn't too much to expect.)
My suggestion is to look for sites without children's facilities, and this can easily be done by avoiding those who advertise 'adventure playground', 'great for kids', etc, etc. You could also telephone the site and ask if they are a quiet and peacful site or a child-centred one.