They migrated all over the North, Midwest, and the West, but I would say mainly the North?
On June 25, 1950, the Korean War began when some 75,000 soldiers from the North Korean People's Army poured across the 38th parallel, the boundary between the Soviet-backed Democratic People's Republic of Korea to the north and the pro-Western Republic of Korea to the south.
Japan was defeated in World War 2, which caused the United States to lead the Allies in the occupation and rehabilitation of the Japanese state. Between 1945 and 1952, the U.S. occupying forces enacted widespread military, economic, political and social reforms.