I'd recommend Kikunoi honten (3 stars) in Kyoto. It's a very short and scenic walk from Gion. The restaurant is beautiful, and very spacious with only private rooms (from what I saw) looking into a garden. And of course the food is top notch with fresh ingredients. Another point to add is that they have English speaking servers who can explain to you the cultural significance behind certain dishes, specially sourced ingredients, and cooking methods, which are all factors that make kaiseki interesting to me.