When in Dubuque, I recommend taking the historic elevator. It is a cheap thrill going up the side of a steep hill on an ancient lift.
I imagined businesspeople crowded in during rush hour back in the day. I bought a postcard, took a video, enjoyed the view and the breeze: there’s not much else like the Fourth Street Elevator.
3rdarm.biz 
There’s Angel’s Flight in L.A.:
https://en.wikipedia.org/wiki/Angels_Flight
http://angelsflight.com/