Murmansk is the last city the Russian Empire founded, and it exists because its harbor does not freeze. A warm Atlantic current keeps Kola Bay open all winter, so a railway was pushed up to it in 1915 and the settlement at the end of the line was named Romanov-on-Murman, after the ruling dynasty. It got its present name in 1917. In the Second World War it was the end of the Arctic convoys, the German army never took it, and the Luftwaffe bombed it 792 times. About 270,000 people live here now, down from 468,000 in 1989, and it is the largest city on earth north of the Arctic Circle.
Almost nobody comes for the architecture. They come for the dark, and what sometimes happens in it. The aurora season runs roughly from 1 September to 15 April, and the sky is the one thing nobody controls. Cloud cancels a night, the polar night (about 2 December to 10 January) leaves a few hours of blue twilight instead of a day, and the one road to the coast can close in a blizzard. Three days is the right length because it gives you three evenings to try: one night is a coin toss, three is a plan. Daytime fills with a nuclear icebreaker, a hilltop monument, a village on the Barents Sea and a morning with reindeer.
Day one is the city, day two the 131 km drive to Teriberka, day three the Sami village trip, and every evening is an aurora attempt. Start on a Wednesday: the icebreaker museum's staff work Wednesday to Sunday. Read the visa and cold tips before you book anything, because getting in and getting dressed are the hard parts. For the country as a whole see Russia.