The most illuminating question I asked any coach was, "What do you know about my son?"
If you subscribe to the "go where they love you school of thought" (and experience has brought me into that camp), this question will tell you who knows him well enough to love him.
Some coaches make offers, especially to pitchers, based on seeing them as little as one time. These coaches gave answers that indicated they viewed him as a commodity or an interchangeable part.
Other coaches really do their homework and go after players only after they decide the players will fit well in their program. One coach had apparently talked to every high school and travel coach my son had played for--and several he'd played against. I asked him the question, and he gave a detailed five minute summary of my son's life, revealing more specific knowledge than I had about how my son's velocity had developed. It was clear that his offer reflected a considered judgment about my son as an individual. (Unfortunately, the academics weren't a good match, so that didn't work out.)
Another question that got a range of answers was, "What is the first thing you would ask me to improve or change if I were to play for you?"
Best wishes,