I think I would go to Korea first, because it's more foreign (to me) than Japan is. Couldn't you take a shorter trip to both countries ? :P
I would most likely go to China first of any Asian country, to bad there's tension between Norway and China (because of the Liu Xiaobo peace price).
Last i heard we aren't allowed to enter the forbidden city, China will deny Norwegians visa to enter. Which is sad, since it's one of the major attractions..