Housed in an imposing looking building, this museum will tell you a lot about the natural and social history of the area. It includes everything from local rock samples to wooden church architecture to Soviet propaganda posters and has a particularly interesting room devoted to clothing and artifacts of the Sami people who inhabit an area stretching from here through to northern Finland and Norway. It's all very well presented, though you won't find any English explications.
www.russianmuseums.info/M914
Lenin Prospekt 90
+7 (815) 242-2679