There were two restaurants I enjoyed very much in Kyoto:
The first is yudofu at a shop across the street from the entrance to the Kitano Tenmangu shrine. This shop has a storefront that sells various yudofu products as well as a few tables on the ground floor and more seating upstairs. You will know you're at the right place if there is a line out the door. We ordered the set menus, about 1000 yen each, because we wanted to try much of the menu. This was my first time eating yudofu, so I will spare you the first-timer descriptions. Just try it.
The second is a soba shop called Arashimaya Yoshimura that made their own noodles fresh. They are located near a scenic bridge. The view from the restaurant overlooks the river and is beautiful and peaceful. We order the nishin soba (has cured mackerel) and also the cold soba with mountain vegetables. I was not a big fan of the cured mackerel because it just overpowered the flavor of the dish. So I removed the mackerel and ate the bowl of soba plain. Both versions of soba were delicious, mostly due to the great noodles. Now that I've had freshly made soba, I am ruined for the dried stuff.