As much as possible! :-) I was pretty happy with everything we did, and I absolutely loved Japan. In retrospect Takayama maybe wasn't the best use of our time, but even that was redeemed by having the best meal of the trip there. We really enjoyed going to a baseball game in Tokyo, but if you're not big sports fans that might not be a must. Nara and the Fushimi Inari Shrine while you're in Kyoto are musts, though. I have a pretty detailed blog post about my trip if you'd like to take a look.
Travel is fatal to prejudice, bigotry, and narrow-mindedness, and many of our people need it sorely on these accounts. Broad, wholesome, charitable views of men and things cannot be acquired by vegetating in one little corner of the earth all one's lifetime. Mark Twain