Narsaq.

There are hiking trails as far as the eye can see, and a short boat ride will take you to glaciers, Norse ruins and sheep farms.

The city has approx. 1,300 inhabitants. Like other Greenlandic cities of this size, recent emigration has put the population into decline, with many inhabitants moving to Nuuk or Denmark. Perhaps this is a pattern, because the area has been inhabited for thousands of years, however not continuously.
On the city limits you can find the Dyrnæs church ruins, discovered in 1932, and Landnám homestead, which is believed to be one of the oldest known ruins from the Norse time in Greenland, from around the year 1,000.

Narsaq is closely associated with the many nearby sheep farms, but you’ll also see other forms of agriculture such as fields of potatoes or turnips.

Dog sledding: No
Midnight sun in the summer: No, but long hours of daylight
Northern Lights (Aurora Borealis): Yes, in a dark sky and with suitable atmospheric conditions