Imperial palace area
Yasukuni Shrine
A controversial shrine to Japan's war dead, housing the souls of some 2.5 million people killed in Japan's wars — including convicted war criminals executed by the Allies. A favorite haunt of right-wing groups in black loudspeaker-equipped trucks. Open daily and free entrance adjacent to Metro Hanzomon line Kudanshita station, or cross the bridge north from Kitanomaru Park. Festivals take place most notably in mid-July and mid-October, which can attract as many people and vendors as it does on New Year's Day when the Japanese come to pray for a prosperous year. It can also get quite crowded during cherry blossom season.
Imperial Palace
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. Unfortunately, the inner palace gardens and buildings are closed to the general public except on January 2 and December 23, when the imperial family makes a public appearance. However, foreigners can also apply online (http://sankan.kunaicho.go...) to join a free guided tour weekdays at 10AM and 2PM. 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 9 AM-noon, 1PM-2PM; 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 Åte-mon entrance; pay attention to the announcement in Japanese and queue up as directed.
Imperial Palace East Gardens
Kept in impeccable shape, the gardens are particularly beautiful during the March and April plum and cherry blossom seasons. 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 Åte-mon 大æé gate near the Åtemachi subway station exit C10. Also an easy walking distance from Tokyo station.
Chidoriga-fuchi Moat
One of, if not "the" most prominent cherry blossom site in Tokyo, and attracts throngs of people in its March-to-April peak season. It is located just across the street from Yasukuni-shrine. Rowboats are also available for one to row along a limited portion of the moat at ¥500 for 30 minutes, ¥1000 for an hour and at a slightly more expensive rate during cherry blossom periods.
Kitanomaru Park
Connected to the East Gardens on the North side is this park. Offering much of the same, it is a convenient way to get to Yasukuni Shrine. The park also houses the Nihon Budokan, which regularly stages martial arts competitions and live concerts, as well as the Kagaku Gijyutsukan Science museum.
Yushukan War Memorial Museum
An odd collection of military paraphernalia including human torpedoes and letters from kamikaze pilots and one-sided descriptions of the war.
Shrines and churches
Kanda Shrine
This shrine has a history dating back to the 8th century and had been highly regarded under the Edo shogunate. The current red-pillared structure has been rebuilt after being completely destroyed in the 1923 Great Kanto Earthquake. The Kanda Matsuri festival, which takes place in mid-May every other year is one of the largest in Tokyo and is a sight to behold. Arrive before noon or the shrine gets packed with spectators.
Holy Resurrection Cathedral
A beautifully-restored 1800s-vintage Russian Orthodox cathedral located near Ochanomizu Station on the Chuo Line. Use the Hijiribashi exit. The Hijiribashi bridge by the exit is one of the better looking bridges in Tokyo and looks moderately attractive when lit-up at night.
Hie Shrine
Another prominent shrine in Tokyo and the Sanno Matsuri festival it hosts in June is counted among the 3 Great festival of Tokyo. Located a five minute walk from Kokkai-gijido-mae station on the Metro Chiyoda line.
Other
Idemitsu Museum of Arts
Has a noteworthy collection centering on Japanese traditional arts
Tokyo National Museum of Modern Art
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.
New Otani Art Museum
Showcases a small collection of French and Japanese arts.
National Theatre of Japan
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.
Japan's administrative center, located around Kasumigaseki and Nagatacho in the southwestern corner of Chiyoda, is full of very un-picturesque buildings. One exception is the Ministry of Justice exit 5 from Sakuradamon, Yurakucho Line, a beautiful 1800s-vintage building that would make any European capital proud. The National Diet Building Kokkai-gijido-mae, Marunouchi Line may also be worth a photo, although its architecture is rather uninspiring compared to other national assemblies' -- even the Tokyo Metropolitan Government has cooler-looking accommodations in Shinjuku.