Other ideas (but feel free to ignore and come up with your own):
- Harry's parents survived but Draco's didn't.
- Hermione is a full blooded wizard and Ron is half or Muggleborn.
- Remus is Harry's Godfather who has been on the run because of his werewolf status, and Sirius has been teaching Defense at the school (lots of good opportunity for drama between him and Snape there).
- Ron is rather popular for some reason and very confident (maybe his dad is the minister or something) and Harry is more of like the side-kick.
- Draco is in Gryffindor and someone else typically in Gryffindor (Hermione maybe?) is in Slytherin. How their personalities are the same as before or different and what friendships exist or don't exist could be interesting.
- Snape is the Gryffindor head of house and McGonagall is the Slytherin head of house.
- McGonagall is the Headmistress and Dumbledore is the Transfiguration teacher and Gryffindor Head of House and deputy-Headmaster.
- Fred and George are studious and Percy is a prankster (possibly in an annoying yet not-funny way?).
I wouldn't really like to see a story in which Harry somehow ends up flung into an alternate reality. I'd like to see a story where this has just always been the way of things.