The store in Sitka is called Abby's Reflection. It's a combo clothing store and quilt shop. The towns in SE Alaska are small and isolated and likely the "must-go-to" quilt shop will be the only store in town that sells fabric - some actual quilt shops and others part quilt shop/part other merchandise.
I grew up in Sitka and IMO, SE Alaska is an amazingly beautiful part of this world and I hope you get to go! Enjoy!!