A great place to go with the kids is Stainmore Railway which runs out of Kirkby Stephen East station. Every weekend they open up the station and the collection of steam and diesel locomotives, along with a play area and café.
Nearby you will find the Northern Viaducts Trail which is a great place to walk or cycle with the kids along a section of old railway line, crossing viaducts and with great views of the River Eden.
Just outside the National Park is the lovely Abbott Lodge with a stunning array of over 40 flavours of ice cream made on the farm from the milk from their Jersey cows. With indoor and outdoor play areas it is always a popular spot.