You could try Serenity in the village of Hinderwell - about 7 miles north of Whitby and 1 1/4 miles from Runswick Bay. It's on here in campsite search - they do accept one or two children but don't be put off by that, it is mainly for adults and is really quiet and peaceful. We woke each morning to the sound of birdsong - bliss! We went the second bank holiday in May last year, the family in the next tent to us had a very quiet 14 year old son and one family in a caravan had a baby, those were the only kids we saw of the whole weekend. There's a pub right across the road from the site entrance which does nice meals at really reasonable prices. It's a lovely site with nice views over the countryside, and the owners are really friendly and helpful. Unfortunately for us the weather wasn't too good while we were there, but it didn't put us off and we will certainly go again
------------- Tigermouse
I have a very temperamental personality - 50% temper and 50% mental
Amazing family weekend with old steam engines, classic car displays, market stalls, and full catering and bar. And camping on site - Save £25 by booking in advance.