Hub Japan lists selections of great kaiseki restaurants in Tokyo:https://hubjapan.io/articles/what-is-kaiseki-ryori-and-where-to-find-it-in-tokyo
I recommend Tofu-ya Ukai to enjoy Kaiseki cuisine in Tokyo. As in their name, the restaurant is famous for tofu but they also serve beautiful and tasty Japanese course. The restaurant is ander the Tokyo tower and the place is isolated from busy area, so you can enjoy silent atmosphere.http://www....
Kaiseki full course usually costs over ¥10,000, but for lunch, somebody place simplify the course and serves at a cheaper price.For example, Inshoutei in Ueno Park offers "Hanakago Gozen" from ¥3,600 including sashimi, tempura, multiple small side dish, miso soup, and dessert.