We mostly went on the scripted tours, which my daughter disliked because they all seemed to have the same script. For those, you (or your kid) can ask about campus safety (can they get an escort back to the dorm if they’re at the library late?) What is there to do in the surrounding town? If the college has football or basketball, you can ask about student tickets. How do the dining dollars work?
For one-on-one visits with a student you actually know (we had the opportunity to do this at one college with a student who went to my daughter’s high school), you can ask more personal questions, like are they happy there? What are things they like and dislike? Did they get along with their roommate freshman year? What do they do socially on the weekends? is there a party scene? Are they happy with their choice of this college? What were some of the other colleges they considered and what was it about this college that made them put down a deposit? What happens if they don’t like an advisor or want to change majors? What are the keys for success in college classes (especially large lecture hall classes that may be taught by grad student TA’s)?
For meetings with department heads, I would have your kid prepare some major-specific questions, info about specific courses, research opportunities, internships, etc., enough to get a good feeling for the program while being respectful of the person’s time.