These schools, like office campuses and other private facilities, are not generally open to the public. They expect visitors to have genuine business there, and people just loitering will usually be asked to leave.
That said, some schools do host public events on occasion, either renting out their facility—such as The Vancouver Island Concours d’Elegance & Motorcar Weekend you linked— or their own events: neighborhood community meetings, lectures, music and theatrical performances, etc... If you check the school's website, there may be calendar listings for these. You'll want to be careful to determine whether the event is truly open to the public or only open to the school community; you can call the school's office if you're unsure. If a public event matches with your schedule and interests, you can get a brief look at the facilities while you're there.
If the school campus does rentals, weddings, events, another way to get a tour would be to schedule one to consider the space for a special event, but it would be quite unethical (and awkward) to do so unless you were legitimately looking to host such an event.
Another idea is to consider that many university/college campuses are, broadly speaking, open to the public (specific facilities and services may not be, but the grounds often are as long as you behave yourself), and there are some beautiful colleges with lovely campuses with lots of green spaces; some even have natural areas. Cornell has 4,300 acres of botanic gardens, for example. So if you adjust your search to higher education institutions instead, you'll find many more options, without the creep factor.