Tokyo has a good offer of museums. If you are into museums you can buy the Tokyo Museums Pass, which gives access to more than 46 facilities.
Some of the main Museums in Tokyo are: The Tokyo Metropolitan Art Museum, with contemporary Japanese artists; the Edo Tokyo Museum, it shows the history of Tokyo; the Tokyo National Museum, with relics from all over Asia; The Kanto Earthquake Memorial Museum, which shows the effects of the 1923 earthquake; and the National Science Museum, centered in natural history.