The food at Mikoan is amazing! You can get a dinner set or lunch set and the lady will prepare different kinds of small dishes on a tray. It is japanese style food and really delicious. Even the rice is more natural and tastier than the normal rice you would get in a restaurant. I recommend you to just buy the lunch or dinner set when you are there. I think it is cheap for a proper Japanese restaurant.
Mikoan is kind of hidden, so please read the descriptions above to find it. The restaurant is very small with about 10-15 seats at the bar. But usually it is not very busy, so you will always find seats if you are not more than 4 people. Personally I liked the atmosphere at mikoan. The music is nice and the place is just stuffed with all different kinds of things (including a "Atomkraft, nein danke" (german anti nuclear power campaign sign which i liked :) )). So you will not get bored there. The only con in my opinion is that the place is a little bit smelly (from the cats) and seems a bit dirty). However, the food didn't seem dirty at all and since you can watch the lady prepare it, I don't think it's so bad.
Usually there is a Japanese woman cooking by herself. Sometimes her mum will be there, too. The woman is kind of shy and quiet, but friendly. I think she might be scared of speaking English because when she noticed we spoke Japanese she got a bit more relaxed and friendlier.
Overall I can really recommend this place. Just considering the food and not the location I think it is the best vegetarian restaurant in Kyoto. So give it a go and see for yourself :)
Cons: cat smell, few seats