I saw this restaurant on Happy Cow before going to Japan in March 2013, and it was very near to Kitano Tenmangu Shrine, which I was visiting to see the ume blossom. I emailed ahead of my visit and the manager was wonderful, he made a reservation for me and would speak to his staff about making a special vegan tofu meal for me.
It was very easy to find and lots of signage. It is on every Japanese tourist's to do list, so gets very busy with Japanese visitors on their holiday to Kyoto. I spoke to a member of staff and showed her my email and after some confusion, I got a table. She spoke to the chef who knew about my visit and they prepared a veganised version of the rice bowl. This would usually have fish stock in, along with the dipping sauce (which they substituted for soy sauce). The food came out fast and was amazing.
The rice bowl had fresh yuba and silken tofu on top, with a bowl of clear soup (I checked what the stock was and was pleased they had taken the time to make it konbu only). Also I had pickles and a plate of different types of tofu. Everything was delicious and I even had a piece of baumkuchen cake (soymilk, of course!). I doubt this would have been vegan, but definitely vegetarian.
The place was very light and the staff were friendly and very helpful. Despite the language barrier, they had an English menu. I think it helped I had a list of what I could not eat in Japanese, which helped the chef understand.
There are souvenirs available here too, and I bought some traditional cinnamon cookies (yatsuhashi), made with soymilk and some sugar and soymilk wagashi, rakugan. There were also lovely calendars featuring their mascot rabbit.
I highly recommend eating here, but contact them ahead of time to arrange a veggie friendly option, as everything will have fish dashi in and bonito on top. Also, there were very long queues when I left (at lunchtime on a weekday), so it is worth making a reservation and going early.
Also, as expected, the meals are very tofu heavy. I love tofu, but maybe your omni friend may not :-)
These are the same people that own the soymilk donut stall in Nishiki Market, which I can also highly recommend - the yummiest donuts I've ever had!