The high season for foreign tourists visiting Japan is definitely during cherry blossom - sakura season. Sakura season is depended on the area in Japan but usually the season in Honshu island starts in the end of March and ends in the beginning of April. Then, the season in Kyushu island is slightly earlier than in Honshu but on the other hand in Hokkaido starts much later, in May.
There are many sakura forecast websites which announce the start of the blooming and the full bloom. Therefore if you want to travel Japan during the sakura season, better to check these forecasts before booking your air ticket. Actually if you are arriving in the end of March, better to arrive at Kansai airport in Osaka rather than Narita or Haneda airport in Tokyo metropolitan area.
Sakura is a special for Japanese and due to full bloom comes only once a year, many Japanese go out to enjoy the full bloom of the sakura. Then, each cities have famous places to see the sakura. If the sakura trees are located in a park, Japanese sit down under the trees to enjoy the picnic. This picnic is called HANAMI or OHANAMI, which usually participants are either friends or colleagues.