The area from Yasukuni Shrine to adjoining Chidorigafuchi Moat in Chiyoda-ku is, along with Ueno Park in Taito-ku, one of the most prestigious hanami (cherry blossom viewing) spot in Japan. (As for cherry blossom at Ueno Park, see the article on the Ueno Sakura Matsuri.)
From late March to early April, Chiyoda no Sakura Matsuri (千代田のさくらまつり) will be held at this area to enjoy the blooming cherry flowers.

Sakura at Yasukuni Shrine

Yasukuni Shrine, which was a shrine presided over by the Imperial Army and Navy until the end of WWII, is famous for its sakura (cherry) blossoms. The way these flowers bloom beautifully and then fall gracefully at once in a short period of time was favored by the military who thought it symbolized their destiny.

Sakura along Chidorigafuchi Moat

Chidorigafuchi Moat is the moat on the northern side of Kitanomaru Park. One end of this moat is the Tayasumon Gate of the former Edo Castle. This gate is located across the street from the first Torii Gate of Yasukuni Shrine.
There's a passage named Chidorigafuchi-ryokudo running along side with the moat, and many cherry trees are planted there.

At night, cherry trees along Chidorigafuchi Moat will be fantastically illuminated, but it'll be very crowded.

You can also see the cherry trees from inside Kitanomaru Park.

Sakura along Hanzobori Moat

At the southern end of Chidorigafuchi Moat there's a street called Daikanmachidori, which also divides Kitanomaru Park and the Imperial Palace. Cherry trees are planted along this street also, though they are not predominant cherry cultivar Somei-yoshino but mostly wild species called Yama-zakura and Oshima-zakura.

If you cross the Daikanmachidori Street and go further south, there is a path called Chidorigafuchi Koen next to Hanzobori Moat. There are some more cherry trees here until you reach the Hanzomon Gate. There will be people partying under the flowers in this area.