The Grange is a famously expensive area of Edinburgh with massive houses. Some of them have turrets and everything! The one the Pope stayed in when he came to Edinburgh is pretty impressive.
I've seen Fred 'the shred' Goodwin's house in the Grange, very nice. Pretty sure Alistair Darling still lives there. JK Rowling did too I think, unless it was technically in Marchmont. It had a security cabin in the garden but it wasn't secure enough to stop the superfans so she's moved out now.
I guess my point is these sort of people - and very trad Edinburgh old money - would be your neighbours. The single most popular car thereabouts is a recent Honda Jazz with a personalised registration plate worth way more than the actual car.
Have you actually gone and spent time in any of these areas you're looking at?