Nuuk (formerly Godthab) is Greenland's capital but not one of its tourist attractions. Kolonihavnen, the small old-town area, makes a pleasant exception to Nuuk's somewhat harsh, apartment-dense, Lego-city look.
If the Nuuk is the only stop you make in Greenland you'll find it quaint, if somewhat rainy, with some fine day hikes and fjordland boat rides nearby. While the city is small by modern standards, with a wealth of land and a paucity of people, most of the population are housed in immense apartment blocks and the urban sprawl is now spreading out along the road to the airport.
Unlike the gentle green swales that nurture several other south Greenland villages, Qaqortoq's colourful houses cling to a steep rocky amphitheatre on the tip of a peninsula. It's south Greenland's main port town and the region's cultural heart with a particularly vibrant art scene.
Qaqortoq is the most convenient base for visits to the lonely Norse ruins at Hvalsey from which you could hike through the dazzling summer flowers to tiny Igaliku, once Viking Greenland's spiritual centre. However access to Igaliku and other great short hikes is generally better from a base at Narsarsuaq or Qassiarsuk.