There are several shops in the Arctic that sell souvenirs such as carvings, shirts and license plates with polars bears on them but nothing beats the traditional work of the local Inuit. I remember children knocking on my door daily, all trying to sell me wood carvings for less than 10 dollars CAN and I am so happy that I opened the door and supported their craft because I now have dozens of souvenirs that remind of the Arctic. The experience was unforgettable and the locals were fantastic :) The souvenirs remind of the place where I can 'honestly say that I experienced the Canadian Arctic'. Breath taking :)
What to buy: Carvings or anything made by the local families. It helps fund them and further solidifies your place in the community.
What to pay: $10 to $200 dollars CAN.
The shops in Longyearbyen does not add valuetax on their goods since Scvalbard is a taxfree zone. But as in other island societies, everything has to be shipped/flown in and there are not much competition so not everthing is affordable.
There are supermarket, outdoor/expedition/trekking gear and souvernir shops. And "NordPolet" the northernmost Norwegian VineMonopoly outlet.
What to buy: Heavily taxed goods as alcohol and tobaco.
Polarbear skins (Verry expensive, but hard to get elsewhere).
What to pay: 24% Less than "down there" on the mainland.