Government Street
From the inner harbour up to chinatown, is the biggest and rather touristy shopping drag. the best way to go is just to wander the streets but make sure you check out some little gems like market square, at the bottom of johnson st. in the summertime there's live music here.
Cuban Cigar
Americans so inclined may want to take the opportunity to pick up a Cuban Cigar or two. Just don't expect to be able to bring any back with you through Customs.
Inner Harbour
The Inner Harbour has artisans selling their crafts during the summer and part of spring and fall as well sometimes, and Bastion Square off of Government Street often has a summer craft market as well.
LoJo
Or lower johnson street has several higher-end fashion boutiques. it's a good place to find local and international designer clothes.
Fort Street
Is otherwise known as antique row. from blanshard to cook streets, fort street is lined with small antique shops and auction houses.
Victoria is full of little shops tucked away in every nook and cranny in the centre. Souvenir shops are all around the Inner Harbour. Although people generally think Victoria is a tourist destination only, there are more than just tourist shops.