Well, the Soviets tried to bomb the city into oblivion in 1944, but thanks to the extensive counter-intelligence work they were bluffed to bomb the island of Vuosaari, which was made to look like the city from the air.
Also the mines of Petsamo produced 75% of all the nickel for the German war machine, so you have your strategic importance right there. Don't know really what the strategic importance was in 1939, but you have to ask the Russians why they were so eager to invade another small nation after the Baltic States. There are always excuses, of course.