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 Seko Naotomo (CC BY 3.0) — via Wikimedia Commons
About 2 million lilies of some 150 kinds on 15 hectares beside Kasui-sai temple. Open only in season, from late May to early July; Asiatic lilies open first, then the hybrids. Entry about 1,100 yen (more at peak).