I love reading everyone's ideas. Varied and all good. I'd love to see the American School or a series about the Founders of Hogwarts.
Personally I think if I were tasked to write something in the HP universe, I think I'd take a minor character and follow them or their family. Dean Thomas comes to mind, we know he's a half blood, we know he survived the battle of Hogwarts, but what became of him after? Still friends with Seamus? Kids etc. What does he do? Maybe I'll write out a fanfic and post it in that section.