Dear footmarks,
I am very sorry for the late reply. I was not sure what you should not miss in Oct, so I asked Chef Tanigawa from Kichisen.
He says Matsutake mushroom tastes the best around that time. Their smell is very unique and special, so Japanese just love them!
Matsutake will be served a lot of Japanese restaurant in Kyoto,in different ways; they will be found in soup or rice very often. Cheap ones are imported ones.
Kichisen kaiseki restaurant serves cut mushroom, you cook over charcoal at your table. That would be something special.
There are no particularly seasonal event at that time, but 25th Tenjin Market at Kitano tenmamgu will be interesting.