Absolutely look at the North Yorks Moors.
Beautiful.
Accessible.
Wet weather attractions an easy drive. If the weather is fine you won't want to go anywhere anyway.
I can't help re. sites as I am a round-the-back-of-a-pub sort of camper. There's a corker next to the Ryedale Folk Museum in Hutton-le-Hole. The only facility I look for is a pub selling cask-conditioned ale, but I appreciate some have higher aspirations.