Rivendale in Ashbourne. Kids will love it, plenty of walks on the doorstep, there are paths through the campsite if they want to take their scooters (mine were too old for that but we saw a few doing it). Walk along the River Dove and they can play in it, its beautiful.
I love catgill campsite at Bolton abbey in the Yorkshire dales, but only out of season. I've been a couple of times late june/early July and during the week there are only a handful of tents on site. It's a nice big field, lobely views, clean facility block and very peaceful. It gets much busier and noisier at weekends though and I've never been in the school holidays.
Hayfield, in Derbyshire. Great hills, village itself is a short walk - has family firendly pubs, shops and a really firendly library. If the weather is really rubbish it is close enough to cities to go for the day.