I'll surprise maybe a few here but first and foremost my visit will be historical, I'd visit all historical place possible and try to learn about japanese culture through their history. I'll do that in the first week and a half of my stay then I'll do for the other week and a half, a trip for visit Gundam related place as well as anime related place then and of course see the Hello Project headquarter.
And with luck why not doing a concert of either Morning Musume or Momoiro Clover Z.
You're right! An historical trip could be fun too! I never thought about that... Japanese culture is so different and it sounds fun to learn about it!