The Yorkshire Moors and surrounding landscapes offer some of the best cycling in the UK, including The White Rose Cycling Route and the Moor to Sea Cycling Route. You'll find these sites useful:
Dalby Forest is only approx 30 mins from The Feversham Arms Hotel, with fantastic walking, cycling, picnic, childrens play area and lots more! There are many off road cycling routes where you dont see a car for miles. Great for the family as a whole, mountain bike hire from the hotel can be arranged - just ask.