There is Wonderland Models that is by Tollcross in Edinburgh city centre, but as far as I know they don't have Breyers. Only the regular Schleich type figures, along with planes, cars and trains models.
The National Museum on Chamber St also has a small range of figures in its shop on the ground floor, but again, no Breyers.
And there is a Toy Museum on The Royal Mile that has only a few lead animal figures in it, mainly 1/32nd scale Britains. Yet again, no Breyers.
And outside Edinburgh there is a private Toy Museum (a family's toy collection now on public display) Hamilton Toy Museum in Callandar, but they don't have any Breyers that I can remember seeing when I visited 2 years ago. Mainly Britains 1/32nd scale again.
I hope you have a nice time in Edinburgh!
They have a few charity shops away from the city centre that you could check if you are walking by. But in all the years I've popped in to any, I've never seen any Breyers in Edinburgh. I have only ever seen one Breyer in a charity shop 25 miles East of Edinburgh in the seaside town of North Berwick. It was a unicorn and foal set and had scratches on them.