A lot of people complain about the rainy season in Japan, but I actually don't mind it at all. Sure, rain can hamper certain activities, but it's a time of year when some of my favorite blooms are out in full force - namely hydrangeas and irises. A couple of famous spots for irises in Tokyo are the grounds of Meiji Shrine and the Nezu Musuem, but outside the urban center and into the suburbs there are still places to enjoy them. When I lived on the outskirts of Tokyo prefecture, one of my favorite iris spots to visit was the Fukiage Iris Park in Ome.
The iris season typically spans the entire month of June, and during that time the park is filled with irises in various shades. My personal favorites are the deep purple ones, but I think it's beautiful having different colors - the irises are set up in almost a color gradient format, with deep purples progressing into lighter purples, all the way to white ones. Throughout the park there are boardwalks set up, so that you can stroll around and appreciate the flowers up close, and on the times I've visited there were also food booths set up selling things like yakitori and yakisoba.
This isn't the biggest or fanciest flower park I've been to in Japan, but it has a relaxed, neighborhood feel - and that to me is part of what makes it so special. It's well worth the 200 yen admission fee they charge during iris season, and if you're in the area I recommend stopping by to check it out.