Just wandering the streets, you will find some great stores and boutiques. I found:
Stassny: With two locations in Salzburg, one for adults at Getreidegasse 35 and another one for children at Getreidegasse 30, this is an upscale clothing retailer offering a more contemporary take on traditional Austrian clothing designs. So if you want to look like the von Trapps for your next Christmas photo, this is the place!!
Braun Confiserie: At Churfurstrasse 4 in Salzburg, this is a shop selling really beautiful chocolates.
Not far from Braun is Schat-Konditorei, at Getreidegasse 3, for chocolates and pastries.
Gmunder Keramik: This is a beautiful store featuring traditional Austrian ceramics with contemporary and traditional designs, including the wonderful stag dinnerware I saw at the Goldener Hirsch restaurant. The company is over 110 years old.