If you choose to go to Fukuoka in November, you could take in a day of sumo. The annual Fukuoka tournament is from November 13 to 27. Mt. Aso is worth a day trip but unfortunately is currently closed to visitors for safety reasons (it might erupt). A day trip to Nagasaki is also a possibility.

In terms of foreign countries, if you can get a Russian visa, how about Khabarovsk? It is a relatively short flight from Japan, like 2 hours, I believe from Niigata or Tokyo. That would certainly be an unusual diversion. I've never done it because of the visa hassle for US citizens.