Kawachi Fujien Wisteria Garden in early June

Is there anything to see Kawachi Fujien Wisteria Garden in June? I know the Wisteria peak is in May. Should we skip it if we can only go in June (June 11 to be exact)

It is not open in June!
You can read about the practicalities here:
https://www.japan-guide.com/e/e4881.html#section_admission

As said, it is not open then. Besides, June is hydrangea season. There are some good other places for seeing hydrangea in the region though.

Thank you. In that case, where to go to see hydrangea? Thank you

Hakozaki-gu Shrine in Fukuoka, Takatoyama Park in Kitakyushu, for example. These are hydrangea sites in northern Kyushu.

The 2 above are quite famous, in addition, in Fukuoka City there is Nokonoshima Island Park, some at Maizuru Park, Uminonakamichi Park, and the Fukuoka Botanical Garden. Nearby, in Itoshima is Shiraito Falls, in Chikushino, the Tenpaizan Historical Nature Park, in Kurume, the Senkoji Temple, in Kitakyushu, Sarakurayama (in addition to its magnificent mountaintop view), and if you're willing to venture out that far, in Tagawa is the Kanayama Sakura Ajisai Garden.

We arrive in Fukuoka in the evening on the last day of their "peak period", so our first opportunity to see the Wisteria will be on Tuesday May 7 - and their website only sells tickets through Monday May 6. Does anyone know if 1) will there still be wisteria to see? (it's nature, so it's not going to switch off instantly at closing time the previous day...I assume there will still be flowers to see, just not as many).....2) Do people still go, the "day after peak season"? (I assume they must)... 3) How do they handle this - just go there and buy a "non-peak ticket"?