You should definitely not miss cherry blossom flowers! In Tokyo, it blooms approximately from early April to mid-April but it depends every year according to the weather.
Some best cherry blossom view spots in Tokyo:
Related to cherry blossoms, experiencing Ohanami (cherry blossom viewing) is one of interesting part of Japanese culture:
In Japan, school year changes in April. So lots of graduation ceremonies are held in March. If you are lucky, you will be able to encounter university graduation where female dress beautifully in Hakama - sort of like Kimono.