LSSM is really top notch. It's grass roots, done by volunteers that want to preserve and share experience with these machines.
Most museums, I'll pick on CHM as an example but it applies to basically any metropolitan museum: by contrast are quite sterile, you can tell they have a ton of money but it's the standard impressive architecture and displays setup that is designed to ferry large groups through relatively quickly but don't impart much wisdom on the participants.
I never got a chance to visit Living Computer Museum but I wonder if that met some kind of high funding to be able to service masses while still going deep hands on.
That wasn’t my impression of the Computer History Museum in Mountain View. (Assuming that’s the CHM you mention.) I haven’t been in maybe 10 years, though. Have things changed?