Cherry blossom is three weeks of it. Flip through the other forty-nine — and watch what's in bloom move up and down the country.
The calendar is the way in. Underneath it sits the ordinary thing — search, filter by month or flower, and open any of the 412 spots.

Photo 江戸村のとくぞう (CC BY-SA 4.0) — via Wikimedia Commons
About 14,000 irises of some 100 kinds in a waterside park on Tokyo's eastern edge. The Katsushika Iris Festival runs from late May to mid June.