Nuuk's latitude makes it one of the most reliable places in the world to see the northern lights. Between late August and early April, the nights are dark enough for aurora viewing; the peak months are October through February. The city has enough light pollution to require a short drive or boat trip to find a dark sky, but the surrounding landscape provides this easily.
The best aurora-viewing from Nuuk involves a boat trip into the fjord or a drive up the road toward the airport, away from the city lights. Several operators offer dedicated northern lights tours in the winter months. The tourist office can advise on current solar activity and forecast conditions. No aurora is guaranteed, but Nuuk gives you a better chance than almost anywhere else with regular flights.