In Edinburgh, there are plenty of places to get cashmere items, not to mention anything tartan :o)
There's a great store down on Canongate just before Holyrood Palace called Made in Scotland or something like that, which sells all sorts of Scottish handicrafts. Definately not the usual tartan tat, and lots of fun items from tea towels to jewelry to pottery to handknit items.
Also, there's always shortbread, and if you are here on a Saturday, you can often get handmade soaps, chocolates, jams, tablet, candles, hard cheeses, hand knit items etc. at the farmer's market on Castle Terrace. Unfortunately you can't take anything with meat, soft cheese or honey to the US, but there are lots of other options.
Also, many stores sell nice, but inexpensive re-usable cloth or waterproofed clothe shopping bags - a unique and fun kind of gift for the shopper back home. Several farmer's market vendors sell them, and Jenners & Marks & Spencers have nice bags.