Sorry, Heian Jingu is for @, water lilies, not @, lotus. They reported water lilies were already in good conditions on 14, 16 and 19 May, this year.
http://heiansan.blog.shinobi.jp/If I apply this earlier shift of 20 days in blooming to the lotus in Hokongoin, you might be able to see the lotus there in good conditions in late June.
In this year, the hydrangea garden at Mimurotoji is scheduled to open during 8:30-16:30 from 1 June to 9 July. On Saturdays and Sundays from 10 to 25 June, they will re-open the garden during 19:00-21:00 (the entry should be before 20:30). Hydrangea should be at their best in the morning, though.
http://www.mimurotoji.com/article.php?id=12In the last year, they reported hydrangea started to bloom on 28 May, were at good conditions on 11 and 24 June, and went beyond the peak on 4 July.
http://www.hanadera.com/2016_2/index.htmlOn the same page, they reported the lotus at Mimurotoji were not in bloom on 28 May, started to bloom on 11 June, and were at good conditions on 24 Jun, in the last year.
