The Gion Matsuri in Kyoto is one of the most famous festivals in Japan. I go almost every year. The best times to go are the nights leading up to the main "parade". This when all the "hoko" carts are lit up with paper lanterns and you can see the carts up close with all the detailed wood carvings and exotic tapestries hanging on the outside. You can even go on some of the larger carts.
This festival is in July and, needless to say, is very hot outside. But this year, the weather was not unbearable at all!