The waterways around Aasiaat make natural kayak country: low islands, narrow channels, open views, and the possibility of whales or seabirds in the same water. It feels less dramatic than the iceberg walls near Ilulissat, but more intimate and easier to read from water level.
Use a local outfitter unless you already have cold-water Arctic experience. Weather can change quickly, and even sheltered channels are serious water this far north.