Meiji Shrine is pretty cool, very historical.
Also if you like history stuff the Imperial palace and the grounds around the area is beautiful, huge moats, the technology museum there and the foundation of the Edo/Tokugawa era castle.
If your into castles, Odawara is a short train ride outside of Tokyo, you'll have to get to Shinjuku train station and take the Odakyu line south, make sure to get the express train.
If you like something different Tsukiji fish market, largest fish market on the planet, get there early, very early.
There's also the museum of art, many artifacts and swords if that is your thing, I have a few Japanese swords and appreciate the craftsmanship
I lived outside of Tokyo for 3 years, I wish I would've travelled more, but really to me most of the really interesting stuff is outside of Tokyo... Have a great trip.