Svolvær has a pretty good-sized shopping mall, believe it or not. Just off Svart Nilsens Gate is the AMFI, a well-known mall chain in this part of Norway. Inside, they have just about every type of store you can imagine, from a COOP "Mega" grocery store, to clothing stores, to art and knick-knack shops, to a state-run liquor store. They even have a "food court" (area with numerous fast-food restaurants) of sorts.
The mall is open Monday - Friday 10AM-7PM, Saturday 10AM-4PM. Closed Sunday.
Another name it's good to be familiar with in northern Norway is Narvesen. This chain of convenience stores is akin to what North Americans and Asians would expect in a "Seven-Eleven" store.
What to buy: The store primarily sells various items to eat and drink, including a limited selection of hot food, and a small amount of toiletries and convenience items. NOK 10 coffee is served from a push-button machine. It's actually not that bad. A "super-special" when we were there was coffee plus a candy item for NOK 15. I decided to go with just coffee.