While you are spending time in Sisimiut or Kangerlussuaq, you can go for treasure-hunting. There is several geocaches in Kangerlussuaq and Sisimiut.
But you can do this treasure-hunting while you are walking the Arctic Circle Trail. TriNitro have made a multi-cache on the trail.
You can start the geocache hunting from Kangerlussuaq or Sisimiut.
You can read more information about Geocaching at the official site.