Hey Chris – good to hear from you.
You are correct in assuming that groups isn’t the right approach here. Groups don’t segregate content as such – they drive permissions but still need to be attached to a category.
A large number of sub/categories is fine (performance-wise) until you get to the thousands, but from a psychological/UX perspective it’s not great to have numerous options – people just don’t know where to go… paradox of choice.
You can build out a rich architecture using tags and tag groups. Check out Tags: category restrictions, tag groups, relationships and It’s Time We Talked About Tags
Will the discussions within each school be similar? i.e. will every school talk about teachers, uniforms and sports (for e.g.) or will they all talk about different things?