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Photo: Ons, CC BY-SA 3.0 via Wikimedia Commons
Has a noteworthy collection centering on Japanese traditional arts.
Idemitsu Museum of Arts is an art museum located in the Marunouchi area of Chiyoda, Tokyo. The museum holds only temporary exhibitions featuring its own collection.
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東京国際フォーラム, Tōkyō Kokusai Fōramu
A massive, modern exhibition centre used for concerts, conventions and the like. On weekdays there are usually several food wagons selling boxed lunches, but aside from this there may not be much of interest to the casual tourist — except, of course, the impressive design. The atrium may be the most well-known symbol of the building, and one is able to stroll up the long, spiral walkway that runs along its glass-and-steel walls. The Tokyo Tourist Info Center, which used to be here, has been relocated to Shinjuku.
皇居 Kōkyo
Surrounded by a series of moats and high walls, the site of the former Edo Castle has been the official residence of the Japanese imperial family since 1868. Reputedly the most expensive square kilometre in the world, which during the height of Japan's bubble was estimated to be worth slightly more than California. The inner palace gardens and buildings are closed to the general public except on the second day of the New Year (January 2) and the Emperor's birthday (February 23), when the imperial family makes a public appearance, and the emperor gives a speech to his assembled subjects. However, foreigners can also apply online to join a free guided tour (M-F at 10:00 and 13:30). If you're feeling lucky, you can also try just showing up at the Imperial Household Agency office located in the northwest corner of the Imperial Palace Park, which is open 09:00-12:00, 13:00-14:00; if there's space, you can join a tour on the same day. Tours are conducted only in Japanese, but electronic audio guides (in English) will be lent to foreign visitors free of charge. At the end of the tour, visitors wishing to enter the East Gardens (see next entry) will be given entrance cards and allowed through to the gardens via a private gate, allowing them to bypass the lines at the main Ōte-mon entrance; pay attention to the announcement in Japanese and queue up as directed.
Kept in impeccable shape, the gardens of the Imperial Palace are particularly beautiful during the March and April plum and cherry blossom seasons. During the Edo period, this was the heart of the Shogun's castle, and you can see the tenshudai, the raised platform where the tenshukaku (main keep) was once located, and an open field that was once the site of the honmaru goten, the Shogun's main residential palace. Entrance is free through a number of gates; you will be given a plastic entrance card at the gate, which you are obliged to return upon leaving; most visitors use the Ōte-mon (大手門) gate near the Ōtemachi subway station (exit C10). Also an easy walking distance from Tokyo station.
国会議事堂
Housing Japan's bicameral legislature, it was built in the 1920s. The most recognizable symbol of the Japanese government, it was built from Japanese building materials, features a pyramidal roof and is surrounded with green areas. The nearby free Kensei Kinenkan (between the Diet and the water) has a nice view on it, and tons of political artefacts to satisfy those interested in Japanese politics. English tours are available on weekdays by reservation only, but the tour focuses almost exclusively on the architecture of the Diet Building such as the origin of building materials or the dimensions of rooms, with little consideration for political procedure or historicity.
東京国立近代美術館, Tōkyō Kokuritsu Kindai Bijutsukan
With a modest permanent collection on display and regularly changing exhibitions, MOMAT is a nice place to kill a couple of hours after you've seen the Imperial Palace across the road. Entry to the nearby Crafts Gallery is included in the price.
国立劇場, Kokuritsu Gekijō
For those interested in theatre arts, the Kokuritsu Gekijyo holds performances in traditional arts ranging from Kabuki, Noh drama, Bunraku puppet theatre, etc. You may want to check the schedule and make a reservation beforehand.