Just to update this thread: My son's first college visits all went well. He met with several coaches and all were positive about his prospects. All the schools asked him to forward an end-of-year transcript and to keep them updated about summer baseball. Being a pitcher makes things a little easier, since they are almost always in demand. Still a ways to go, but it appears son is fishing in the right ponds.
As for the question I started this thread with: The visits played out in just about every possible fashion. At one school, the coach came down from his office to meet my son before I could make my exit from the building, and that coach asked me to stay for their meeting. At another school, my son met with the coach on his own, then son texted me to join them for a while after that. And at a third school, son went to coach's office by himself, but coach asked him to call me in for the entire meeting.
Based on my limited sample size, for future visits I think son will stick with the plan of going to coach's office on his own and introducing himself. He will let coach know I am nearby and let the coach decide how he wants to proceed. That worked well so far, anyhow. There is not going to be any scholarship money or other financial aid at stake, and every school my son met with is one where academically I'd be happy to see him enroll. So to my mind, the baseball decision is almost exclusively my son's to make (with a little parental guidance, of course). The boy rose to the occasion very well. I was proud of the way he handled himself.
Thanks again to all who offered advice in this thread. It was extremely helpful.