There are many Newfoundland-specific shops in Corner Brook, as there are all over the island, but a good concentration of them are on Broadway. You'll be able to find Provincial Flags, Republic of Newfoundland flags from the era when the Island was a separate country, traditional and contemporary music, books, and art. Currently, cheeky Newfoundland separatist t-shirts are popular. They usually read: "Free NFLD", or "Newfoundland Liberation Army". You'll also be able to pick up t-shirts and the usual items of the Tourist variety at these shops.
If you're looking for non-Newfoundland shops, there are two downtowns relics of the pre-amalgation communities centred around Broadway in the west part of Central Corner Brook, and West Street in east Central Corner Brook. These areas have the charm of small communities and give the visitor a more accurate feel for the Newfoundland culture.
As for the fare of generic malls, you can find those inside Corner Brook and on the outskirts of the city. Inside, there's the Valley Mall and Millbrook Mall, nestled right next to each other in the centre of the city where Main Street becomes Herald. On the outskirts, there's Murphy's Square, a collection of big box retailers, and Corner Brook Plaza, a typical city mall with a second floor in the works.
