Within a short drive there is:
Clapham - delightful Dales village with a playground plus a buggy friendly woodland/lakeside trail that has lovely views leading up to Ingleborough Cave.
Settle Playbarn - excellent soft play area that unusually serves good food & drinks (not the Whacky Warehouse variety). One suggestion for a lovely day out is to get the train from Ribblehead (stunning views) to Settle then do the short walk to the Playbarn. Settle also has a Booths supermarket with a playground next door and an excellent Falconry Centre (make sure you don't miss the demonstration times.)
Kirkby Lonsdale - take the bus to Kirkby Lonsdale, a picturesque local market town, where you can play in the river, walk along a safe off-road path to the town and have a bacon butty/ice-cream at the famous Devil's Bridge picnic spot.
Morecambe - children's paradise! - playgrounds all along the promenade, fantastic eye-catching sculptures everywhere, Happy Mount Park with train and splash park (seasonal, take change of clothes and/or swimwear.) Keen cyclists can cycle all the way there along the flat off-road route from Bull Beck car park, near Caton. Cheap, child friendly café at Morrisons Supermarket.
Williamson Park - a 50 acre park in Lancaster, has a tropical butterfly house, other small animals, a fun playground & other bits to explore - handy place to visit when the weather is iffy as it has some sheltered parts. It also has lovely views over the North Sea and the Lake District.
Grange/ Flookburgh - (just under an hour's drive but worth it). Grange is a beautiful market town with a fantastic bakery/café called the Hazelmere, where you can buy a picnic & get free old bread & go to feed the large array of ducks on the ornamental lake. It also has a great playground, overlooking the picturesque bay. From there, it is a 2 mile drive to Ducky Park Farm at Flookburgh which is a children's farm with indoor soft play area - great for wet days. From Grange, you can also take the short but stunning train ride to Arnside across the estuary.
Skipton Castle - Over 900 years old, it is one of the most complete and best preserved medieval castles in England and is well worth a visit at any season of the year. The refectory in the church next door sells cheap, delicious lunches. Skipton also has a good swimming pool and lovely walks along the canal.
Close-by Skipton is Embsay Railway, from where you can take an old-fashioned small train ride to Bolton Abbey and enjoy the fun of Hesketh Park Farm.
Over in the Lake District, about a 35 minute drive away is the wonderful Lakeland Maize Maze which is a great place to take children even on wet days as it has an indoor softplay area, climbing wall, tractors, go karts and sandpit as well as all the animals, interesting playground and mazes (including one for younger children) outside. Check for seasonal opening times.
The Forbidden Corner at Leyburn was voted top children's attraction in Yorkshire.