If you're looking to escape the ball pools and soft play, then a short drive out will ensure the kids [and you] will be entertained. There's the real adventure of Go Ape in Dalby Forest, or the heights of Arial Extreme at Bedale. You could consider Flamingoland and Zoo near Malton, Eden Camp in the same vicinity or maybe Beacon Farm at Sneaton, near Whitby would be more up your street.
If you like water, then head out on Cook's Endeavour cruise trips at Whitby, or while you're in the area paint your own pot at Doodlepots in the town. There's the North Bay Miniature Railway in Scarborough, the Museum of Victorian Science in Glaisdale or consider Pesky Husky Trekking at Staintondale.
If you'd like to try off road driving, quad biking, clay pigeon shooting or a segway trail, see Yorkshire Outdoors.
There really is a myriad of family activities in the area, so get Googling or click here to search on the North York Moors Website.