Apparently Rowling thought of Hogwarts before moving to Edinburgh - but it seems a bit of a coincidence that Heriots school is right next to the graveyard with Tom Riddle's grave:

https://www.pottertour.co.uk/blog/george-heriots-school-harr...

Mind you - I'm not really that big a Harry Potter fan but I did live in that part of Edinburgh for many years and my son went to Heriots after adventures at other schools...