another vote for the kids playground at Bamford – if you cycle away from Derwent across the playing field and under the railway line you pop out in a garden centre carpark – ice creams or hot chocolate and gold fish to watch – my kids are small teens now but the walking shop there used to be one of the best places to get small kids proper outdoor gear
if based in Bakewell then Chatsworth House is an obvious attraction but if not your thing it still has a great playground for kids – charges but not full house entry
someone mentioned train to the Ponds Forge rapids in Sheffield as wet weather venue, by car Weston Park museum, Sheffield is excellent for kids and very easy from the Peak, though expect to spend some time looking for a parking spot
left field – if travelling from down south then Twycross Zoo sort of near Ashby de La Zouch and the M42/A5 is a good long stop off on way
edit favourite cafe – Hathersage Pool and you don’t need to go in – still like Grindleford and will always pop in but the guy responsible for following up on the notorious instructions to customers died around 7-8 years ago ? (Phil?) and really they should have gone with him