Picnics under the cherry blossoms (o-hanami) are an important part of Japanese culture. So important that the Japanese meteorological office produces a forecast of cherry-blossom season every year!
The 2014 cherry blossom season will start in less than one month. To better synchronize your visit of Japan to the famous blooming tree, please consult either of those two official websites:
The website cheriblossom.com also shows in-real-time cherry blossom forecast (Thanks to Sakuman for the info)