Check out Ede and Ravenscraft in Frederick Street!
Walker Slater has a horrible staff. Lot's of Tweed suits though, although the quality is not impressive.
There is another shop, Stewart Christie in Queen Street, near the Ede and Ravenscraft shop. It is much more oldfashioned than for instance Walker Slater. Much more charming, if you ask me.
If you have a car and plan a tour to the highlands as well, check out The House of Bruar near Blair Atholl. A big shopping village offering mainly scottish clothing (Tweeds, Cashmere etc.).