We went to this restaurant that was recommended by the concierge at the Hyatt Regency and couldn't have hoped for better. First, the location - Shinbashi st., lined with beautiful Japanese old houses that create a dreamful atmosphere. The interior is also outstanding - simple yet amazing and creates an ambience that is an experience in itself. And then the food - delicious, served gracefully, great service - simply top notch. They have English menus and were also very helpful with accommodating my gluten allergy. If you don't read Japanese you will find it hard to locate the place unless you have a picture of the entrance - we used the one on the tripadvisor iPhone app. Reservation recommended.

We first went to this restaurant on the recommendation of Hotel Mume. The second time we went was on our own, on our next visit to Kyoto a few weeks later, after dreaming about it the whole time.
It's in Gion, on a street lined with traditional buildings. We carefully compared the photo provided by the hotel with the sign and door, and then had a moment of uncertainty when the door opened into a tiny genkan (entry way). But in a couple of seconds, the smiling hostess greeted us and showed us to our seats at the bar in the large room just behind the entry. To our relief, the seating is arranged with a space under the bar so you can sit with your feet on the floor instead of tucked underneath - and yet you are still at eye level with the service staff.
There is an English menu, handwritten, and, like the Japanese menu, it changes with the seasons. The food is really outstanding, among the best we had in Japan.
The hostess speaks excellent English.

Yata is the sort of restaurant one occassionally found by chance in the days before Chowhound and, yes, Tripadvisor, and refused to even tell your mother about. On a street of traditional wooden buildings in Gion, it can't be found without a picture of the entrance, so nondescript is the exterior. The interior, as detailed elsewhere, is quite another matter. The tasting menu, which changes each month, is full of delights. We had two completely different menus in our two visits, and there wasn't a miss in the lot. Michelin star level.

Don't tell your mother.

we went to this restaurant on the rec of our Ryokan Shiraume. It's on a main road, but difficult to find if you do not read japanese (ask for help). The setting is lovely, seats mabe only about 15 people or so, very personable space and the food is delicious. definitely go for the wasabi mayonnaise crusted shrimp! All japanese people when we went, and the waitress luckily spoke some english and so was able to fill us in on the seasonal ingredients in everything. make a reservation in advance

Yata was another outstanding recommendation from Hotel Mume. A lovely exterior, simple exterior on the best strip of Shinbashi-Dori and stunning interior - a room with a long counter around the kitchen and loud greeting from the staff. We were sat around the counter in the back room - possibly a bit plain when compared to the front, but we were the only foreigners in the back room and it was a very special venue indeed.

Overall one of the most enjoyable dining experiences of my life - great food (9+1 courses), outstandingly attentive and friendly service, and a genuinely charming atmosphere as couple by couple eventually over half the room quizzed us, asked where we were from, were impressed with our chopstick skills, gave us some of their dishes to try (as we asked the waitress what they were), or even gave is their business cards.

The 9 course menu was spectacular, including excellent sashimi, sea bream cake and pea broth, scallop, green tea ice cream, etc. We couldn't resist a side order of the delicious grilled beef either. And the wheat germ or grilled bamboo weren't things we would have normally ordered but were very tasty surprises on the 9 course menu, which was perfectly paced so that at the end the 2.5 hours seemed much shorter - never felt like we were rushed, nor were there moments we were waiting around. Great food, service and atmosphere. And much less expensive than you would expect for such an experience (~Y10k per person).

Finally, the bar upstairs is great also (seats 8), with good cocktails and, of course, excellent staff (and reasonable prices too).