Thanks all. It certainly sounds feasible, and with similar frustrations to cycling somewhere like London (I find it hard to believe driver would be as aggressive as here, though...) I wasn't planning on bringing my own bike, but rather trying to arrange a rental locall, and am not sure I'd go to Tokyo this time. Anyway, it's still very tentative!
So thanks again. I'll certainly consider this.
Oh, on other Q - at 6'1", I often found myself feeling very tall when in Japan. Am I likely to have problems finding something with a long enough seatpost?