"The northernmost permanent human settlement, which is not a scientific or meteorological station, military outpost, is Siorapaluk, an Inuit (Eskimo) village in northwestern Greenland, situated at 77degree47'N, 70degree46'W. The number of inhabitants is 87. ... Alert, a settlement of 5 inhabitants in Ellesmere Island (Northeastern Canada), 82degree28'N is seen by many as the actual northernmost human settlement, but this is more of a military and meteorological station, like the settlements established in Svalbard during the XXth century, which are mining or research communities.
The northernmost city could be considered Troms, Northern Norway, at 69degree34'N and 61,987 inhabitants."
http://news.softpedia.com/news/Human-Settlements-to-the-Extremes-the-Northernmost-and-the-Southernmost-45696.shtml
The distance of each of these from the North Pole is found by using the difference between their latitude and 90N, and multiplying by the surface distance corresponding to 1 degree of latitude.
"Each degree of latitude is approximately 69 miles (111 kilometers) apart. The range varies (due to the earth's slightly ellipsoid shape) from 68.703 miles (110.567 km) at the equator to 69.407 (111.699 km) at the poles."
http://geography.about.com/library/faq/blqzdistancedegree.htm
As we are near the poles, we can consider the distances as
being close to the polar values. Using the above conversion:
Siorapaluk is approximately 1365 km from the geographic North Pole.
Alert is approximately 841 km from the geographic North Pole.
Troms is approximately 2282 km from the geographic North Pole.
Decide how you want to define a human settlement, and you can take your pick!