Would thoroughly recommend taking your kids to an indoor climbing wall. Either get yourselves and kids booked in for a lesson to get you started or it's also a great alternative for birthday parties.
I've been going to a place called Redpoint in B'ham. The instructors are friendly and great with children. They have party rooms upstairs so you can have cake and food etc after if celebrating a birthday (or even order in pizza).
I've been climbing for a number of years, it's fantastic to be able to share a sport with your kids which you get a real sense of achievement from.
Even if you haven't got a head for heights you can grab a hot drink and a cake and watch your little ones climbing the walls!
Redpoint do have a website - it's worth checking it out.
redpointclimbingcentre.co.uk