With the yen at historic highs, the world's top destinations are the Japanese traveler's oyster: New York, Hawaii, France, Italy – pretty much anywhere is much cheaper than it used to be.

Even then, the trip was almost called off. The Japanese government only gave its formal approval supporting the team, JFA officials and fans to visit the country on Tuesday: Tokyo has strongly discouraged residents from visiting North Korea citing economic sanctions imposed by Tokyo after a missile launch in 2006 (North Koreans are banned...