A lot of very nice computer collections are parts of bigger ones in larger, less specialised, museums.
It’s rare for museums to keep artefacts operational. The ones that still work are usually treated as the big attraction because they demand attention and maintenance.
I was recently in Bletchley Park, where I saw a partially working Bombe (they only run it partially because of the wear), and their smaller computer museum (there are a lot of machines that are available for visitors to play with) and the one in Cambridge, which has classrooms with BBC micros, as well as many other interesting machines - Suns, SGIs, Amigas, Ataris, Spectrums, and even a Lisa, which had a boot issue.
I have to say the kids in the last two seemed thrilled to play Lemmings on Amigas and Archimedes machines. Not a PDP-1, but still cool.