I second everyone who's said check the weather- I went to Hakone without really checking weather reports, and spent two days wandering around in the fog. Literally. It made for some cool pictures (like a red tori just barely visible in the mist), but I definately did not get to see Fuji.

Also, definately check out the fish market. You have to get up really early, but it's worth it. (unless, of course, you have a really weak stomach.)

I'm interested in theater, so while I was in Tokyo, I was happy that I was able to catch a children's version of Japanese opera (the name of it is escaping me). They rented headphones through which you got an English translation of the show as well as the "talk" beforehand explaining the style of theater. I believe that was at the National Theater. Worth the time, especially if the weather isn't great out.