Hello Brian.
One place I'd highly recommend for you and your daughter is the Ghibli Museum:
http://www.ghibli-museum.jp/en/
Usually very difficult to get tickets, but maybe the Mandarin Oriental concierge could help you score some?
Another place she'd probably like is Kidzania, a place where kids can pretend to be adults for a few hours:
http://www.kidzania.jp/tokyo/en/
That's another one where you might enlist MO help in getting tickets.
And I probably wouldn't make this recommendation for anyone other than someone travelling with a five year old girl:
http://www.puroland.co.jp/english/welcome.html
It's kind of like a small indoor Disneyland, only with Japanese Hello Kitty characters.
Hope you figure out a schedule that will give you some very special memories with your daughter!