I found out about this festival when I visited the very cool Kite Museum in Nihonbashi. It’s not in any of the festival listings I usually check, but I quite enjoyed it. There are tons of kids flying cute homemade kites, as well as the more serious aficionados from the kite association.
The festival seems to be held at different dates depending on the year, so check the Japan Kite Association’s homepage. It starts from 9 AM and finishes around 2 PM and is held in the “Niji no Hiroba” between the Senju Shimbashi bridge and the Nishi Araibashi bridge near Kita-Senju Station. Call (03-3880-5985) for details.
Another excellent festival is the Hamamatsu Matsuri in Shizuoka prefecture, held during Golden Week every year. http://qjphotos.wordpress.com/2008/04/05/hamamatsu-kite-festival/