It's been nearly 40 years since I was there, but a couple less-visited cities in Japan that I can recommend are Nagoya and Nagasaki (you might need to take some trains, but the train ride to Nagasaki is among the most picturesque I've ever taken!). Some highlights (assuming they're still available -- remember that 40 years caveat!):

• Nagasaki: huge market with every type of store imaginable; I picked up some piano and brass quintet music there.
• Nagasaki: old Dutch Quarter, which survived the worst of the bombing. Fascinating contrast in architecture with the rebuilt part of the city.
• Nagasaki: the Peace Park, of course. One of my most memorable experiences ever was when a Japanese gentleman wanted to take a picture of his family with the Americans at the memorial.
• Nagoya: the castle. Large enough to be interesting, small enough to not take all day.
• Nagoya: the NHK tower, for a nice view of the city.
• Nagoya: the Noritake factory and museum.
• Nagoya: at least back then, no airport departure tax!