Popular events/things in the summer of Japan are,to my memory, big summer festivals such as "Nebuta matsuri", "Kanto matsuri".
But you might be able to find more interesting thing.
That is "many cicadas singing" in a park, forest wherever they can find to sing.
Without this pepole might be unable to feel that real summer has come.
I will try to take a photo of a cicada next time if I can catch it.