Kyoto is known for many things: temples and shrines, it's rich history (it used to be the former capital of Japan), Geishas, and of course, food. Dining in the Gion district used to be very exclusive (and in many ways still is), however some restaurants are opening their doors to tourists. One of those establishments is Okumura, who has a delicious French Kaiseki course, with omakase lunches starting at 5,000 JPY, and dinners from 10,000 JPY. Cheap compared to the $3-400/person meals out in LA or NYC. The great thing about Okumura is that they offer an English menu, so no awkward lost in translation moments here. Make reservations in advance, most small restaurants in Japan don't take walk-in customers.
We enjoyed the 5,000 JPY lunch and were very satisfied; I can't imagine what their other sets deliver-- I'm sure even more delicious and fulfilling.
Restaurant Gion Okumura
Address: 255 Gion-cho Kita-gawa (Gion Kiritoshi-agaru), Higashiyama-ku, Kyoto-shi, Japan, 605-0073