Another wannabee Trebizonian here. They got to learn to surf, have beach parties and date boys, although some of the plots were a bit over-contrived and fantastical! I liked the Head, Miss Welbeck, who most of the students seemed to have girl-crushes on.
St Clare's and Malory Towers: only in adulthood can I see what horrible bullies populated those places. Poor old Gwendoline Mary had every bad character trait dumped on her, was the scapegoat for every situation going and was the girl her 'friends' loved to dump at the end of every term. Alicia, the alleged 'cool' girl of the class, was much more of a piece of work than Gwen - vindictive and a nasty bully - yet the narrator clearly means our sympathies to be with her. She's awful!
As for St Clare's, same old with Alison the 'feather-head' who is continually patronised for her intimate friendships (same as every other girl in school, then) and love of the cinema. And what's wrong with that, may I ask?
Oh, and Mrs Florence's school in the Katy books where they survived on a horrible diet of 'pudding', their water froze in the pitchers and 'flirting' was frowned upon with a deadly, puritanical zeal. Yeuch! That said, Rose Red was and remains one of my favourite characters ever.
Maybe as a kid I was far too heavily invested in these books, but can I just say that I love this thread: thank you OP!