Your post made me think of the “think[box]” at Case Western:
which, they claim
I don’t have any first-hand experience with it, but we visited it when we visited the school.
I suspect many schools have some kind of facilities like this (or things they try to build up as this). So you should research some to get more info on them, to see which meet your desires. You can search for things like “maker space” or “fab lab” or such.