All of the above!
If they're into Vikings, then the Jorvik Centre in York would be a hit.
Bolton Abbey, Billy Bob's Ice Cream Parlour
Eureka (Halifax) ! - if it rains, maybe combine with The Piece Hall
Quicker trisp out actually in Leeds - Abbey House Museum, Kirkstall Road and The Royal Armouries (Armouries are great fun if the free boat from the Armouries to the station is running).
Fun place to eat - Rosie's Diner, Kirkstall Road
Bit further out - Yorkshire Sculpture Park (much more interesting and child friendly than it sounds), £10 to park for a day, but park entry is free. OK cafes, but only 5 mins from the superb Blacker Hall Farm Shop and Cafe
I hate Forbidden Corner, but appreciate that I am in the minority
Scarborough or Whitby if you want a beach - I prefer Whitby
Brimham Rocks (NT), Otley Chevin, Hardcastle Crags (NT), Golden Acre Park, Temple Newsam for running around and exploring. BR and HC have lots of rocks to scramble on. TN and GAP are actually in Leeds, OC only a short distance away
Ilkley Lido, and Betty's.
There are trampoline parks all over the place around Leeds, also a climbing wall, and an extremely high wall at Brighouse if that floats your boat.
Leeds Clip n Climb is a combo of soft play, climbing wall and trampoline park.