This question has answers at several levels. I’m assuming you are asking as a parent, so that’s where I’ll start.
First, look at the programming that’s being offered. If there are choices, be intentional about where you end up.
Second, if you have specific questions you want answered, make sure you get to the right forums/people for that. It is likely that a session on athletics will answer most of your questions for example, but if you want the ins and outs of whether you can be exempt from sport for a season to train with a local club team and how that’s coordinated, make sure you approach the AD while you are there.
Talk to current parents and students. And in particular, ask to be directed to parents who might have similar concerns, whether it’s how far you can commute as a day student, sports, etc. Also, ask open-ended question and listen careful to the answers. Questions like “how did you find the adjustment to being here your first year?” "What surprised you? What was the hardest part? How do you stay in touch with your kid/parents? What do you love most about this school? What kind of person thrives here? In many cases, these are the questions you were probably asking when you were visiting for tours/interviews, but this time round, you’re the buyer!
It is often worthwhile to understand how discipline works.
Students should pay attention to how they feel in the ckassroom, dinig hall, etc. Does this place feel clique-ish? Are these kids their tribe? Did anytime put them off? If anything goes “wrong” (person she’s shadowing has a test), how is it resolved? (Kids will likely resolve these things on their own.)
There are a lot of people who feel the decision is 100% up to the kid, and while I mostly agree with that, remember that at some point, you are likely to be at odds with the school about something. This is real life. When that happens, it’s really helpful if you believe in what they are doing and that they are good people.
So be present, listen carefully (not just for affirmation of what you think to be true), and enjoy!