There are tours of limited portions of the Imperial Palace. These are free but need to be booked in advance (online, English website available). There are also two days a year, around New Year's, when the palace grounds are open to all.

And 9am at Tsukiji by all accounts is no better than 11am, it's more like 5am. Not that I would know, I've never been and never intend to go!

Does most of the sightseeing in Tokyo really revolve around shrines/temples? I've never noticed that, maybe others have.