If you can only have five to seven days, I would recommend either Guam or Saipan. Both are only three hour flights from Narita, and are affordable compared to Okinawa. As Jonathan said, Okinawa can be quite pricey, and the best dives are to be found well away from the main island, and just getting there can take up the better part of the day. If you can afford it, well, you're lucky, because Okinawa diving is fabulous.
It depends on whether you plan to take the course in English or Japanese. If you are a fluent Japanese speaker, I would suggest Saipan. It's my understanding that the visibility is a bit better than that found in Guam. I had great fun with Aqua Del Rey
www.aquadelrey.com The instructor, Teru, speaks English quite well, but I don't think it's his first language.
Since Guam has a large US military base, I am sure there are more than enough dive shops catering to English speakers. Come to think of it, I think there are quite a few Scuba Board regulars in the area.
Keep in mind, Octobeer 13th and November 3rd are Japanese holidays, and many schedule their vacations around those three-day weekends (though nothing like Golden Week and Obon and the New Year holidays! Although Golden Week was rather muted by SARS this year...)