Golden Square near Helmsley is fantastic for your age range of kids, really good play areas in a lovely setting. Think there is a pub but maybe not within walking distance with little ones
Hooks house Farm at Robin Hood's Bay, yorkshire coast. We had a fab week there last September. Owners very friendly and helpful - it's a short walk into the town where there are about 5 or 6 pubs, lovely walks, quirky shops - good food at pubs - also The Fylingdales Inn nearby. Most places are dog friendly too if that matters to you??