We absolutely love museums and have done a lot of smaller, more random ones and actually avoided the big London ones as we can only go in school holidays and the thought fills me with dread!
Wherever we go for a holiday, to meet friends or visit family, city breaks etc, we find the nearest museum/gallery etc. I prefer low key, free, non timed stuff but so mix in some of the more exciting flashy ones.
Some of our successes-
Techniquest - great hands on stuff, nice open spaces, good physically active bits and plenty to do even if busy
National Museum in Cardiff had a great Dino exhibit when we went, lots and lots of interesting bits and a friend up art exhibition that dc surprisingly got quite into
Leeds Armouries - amazing children's room with arts, crafts and dress up
Leeds Museum was great, lots of dressing up and play space
The museum at Jimmy's in Leeds has a while floor of hands in children's stuff, dressing up etc but unfortunately it's got a v gory welcome exhibit which spoilt it for the DC as we arrived. I want to go back now they're older and braver.
Worcester had a little local museum that had good colouring and some kids bits
Eureka in Halifax is amazing. Incredible hands on exhibits, workshops, outdoor play. My DC haven't been for years but still talk about it
Winchester Science Centre is a really good hands on place, wasn't too busy when we went too.
We've done a lot in Devon on holidays -
Tiverton Museum was surprisingly good - good hands in and dress up, great train to visit, only adults pay
RAMM in Exeter, great spaces from roaming around, good kids' provisions and loads of workshops and extra stuff in the holidays
Topsham Museum was sweet and had a craft workshop in the hols for kids