The Small Cable Railway Museum is a niche but fitting Innsbruck stop, because mountain transport is central to how the city works. It tells the story of the Nordkette railway and the engineering that links an urban valley floor with high alpine terrain in a matter of minutes.
Do not plan a whole day around it. Instead, fold it into a Nordkette outing, especially if you are interested in funiculars, cableways, or the way Innsbruck turns steep geography into everyday infrastructure.