I love museums and would recommend many of the ones that I have been to, but you need to be do some research before you go if you want to access them to the full.
The most recent museum exhibit I visited was about Egyptian mummies at the Oxford Ashmolean museum. I had a mixed response from the staff about touching objects. One person abruptly said I wasn't allowed to, but then someone else came along later and let me touch some of the objects.
She explained that there was an audio guide available and that there were certain times when the museum conducted guided touch tours, but that those took place on specific days.
However, I had an enjoyable experience at the museum and enjoyed touching the objects with the more helpful member of staff.
I think the exhibition would be suitable for children and young people because it would be an interesting and fun way to learn about a subject that they may be studying at school. I would visit the Ashmolean Museum again if there was a suitable exhibition that was accessible.
The Pitt Rivers and Natural History Museum in Oxford also provide a wonderful and exciting experience for all visually impaired visitors, for example.
It offers an audio guide and they also have braille labels on many items. A huge number of the exhibits are meant to be touched, such as stuffed wild animals, fossils and skeletons. There is so much to see that you can happily return again and again. I highly recommend it for children.