Some of the major seasonal festivals during rainy season are based around the hydangrea flower (called ajisai in Japanese). The ajisai festivals are on all over Tokyo and beyond around the middle of June. One of the good ones starts on June 11th and runs through until the 19th of June at Hakusan Shrine. There are 10,000 plants on show and entrance is free.
Look out for similar festivals in your neighbourhood – entrance is likely to be free too.