I love having people shadow me, especially on longer running shows where I've developed a comfortable routine. I normally ask that the person see the show first so that they understand how what I'm doing connects to what the audience sees, and also so that they come in with questions. I try to narrate what I'm doing as much as possible, having talked briefly before so I can judge what their interests are/experiance is. I'm not a huge fan of someone spending three-four hours with me and never saying a word - have thoughts, have questions, have opinions, please.
On my last show I had a playwright shadow me before she gave a post-show lecture (not the author of the show I was calling) and it was so much fun to answer her questions about how I time out specific cues each night, feeling out the mood of the actors and audience, as well as talking with her about the notes I was taking for the actors. It was nice to talk with someone about maintaining the show, rather than the technical part of things other stage managers are interested in.
The assistant to the director on that show was an actor who had just finished undergrad and asked if she could shadow as well. Again, I had a great time, her questions were very different, she'd never seen someone call a show before so it was really about going back to square one. Because she had been with us our whole rehearsal and tech process we got to talk about what I look for in rehearsals in anticipation of calling the show.
Last year I had a very precocious five year old watch me call an act while his father was onstage (and his au pair standing next to me). Also fun, better than students who may get more out of it but I leave unsure of what they learned or were interested in.