Singingbee, Serenity campsite at Hinderwell not far from Whitby was very pleasant when I went a few years ago. I can't remember the cost, but I don't go for expensive sites so it must have been reasonable. Quiet after 11pm, facilities were spotless and there's a good chippie and a pub within walking distance too. Not sure about dog-friendliness though; site reviews or website should clarify that.
http://www.ukcampsite.co.uk/sites/results3.asp?search=serenity&by=sitename
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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.