Maybe somebody will point to one, but my googling hasn't turned up such a place. If it doesn't exist, it needs to. You could have a few dioramas, like a natural history museum, depicting the proud lift operator, or the chatty switchboard operator. Even more so, there should be demonstrations. There should be a switchboard for the kids to try their hand an operating. Something tells be that it was more complicated than it looks.
I can imagine the wonder on their faces as the docent, (perhaps dressed like Ernestine) explains that in the olden days, you had to rely on a real human being physically connecting the wires each time you wanted to call.
While I'm tempted to list things like buggy whip manufacturers and blacksmiths, the fact is those still exist, although mostly as hobbyists. I doubt there's a phone company that let's you opt into having a switchboard operator, just for old times sake. I also think it should be the kind of place where grandma or grandpa can share actual jobs they may have had one day, so they need to be relatively recent.
I suspect the museum would be fairly small now, but whoever starts one better leave a lot of room for expansion.