A place very dear to my own heart is Rakusui, a short walk from subway Keage station in Kyoto.
A long long time ago, Rakusui was the principal residence of the Fujita family, the 3,300 square meter garden designed in 1909 by the 7th Ogawa Jihee, and just recently in 2003 has been restored by the 11th Ogawa Jihee, who has inherited the landscape gardening technique Ueji. He says "Think easy, not difficult things. Designing gardens which heal your mind and make you yawn when you see them with an empty mind—that is my style." The garden is what brings most people to Rakusui. The pond in the middle of the garden was designed in the shape of lake Biwa, and even draws water from a channel through the mountains strait from the lake. The first time I stayed there with the family, one Aunty asked if it was OK to drink the tap water. The staff replied that not only was it OK, but they believe it to be the freshest tap water in Japan. After a drink myself, I can't help but agree.
The garden was designed to make the viewer feel relaxed from the very bottom of their hearts. The tall trees along the fenceline hide all surrounding buildings, and only the tips of the mountains behind are visible, giving one the feeling that you've really left Japan behind. There is a nice open lawn area on the lobby side, and seats for viewing, so even on a cold day you can sit outside and soak up some sunlight.
behind the pond is a building called a Gasendo • 画仙堂, which is a 'shrine of picture immortal' (according to the information I am currently reading). Apparently it came from China about 280 years ago. Religious ceremonies conducted there nowadays (mainly wedding ceremonies), are done by the priest from Ootoyo Jinja, a small shrine on the Philosophers Walk.
The cook at Rakusui is also very good. Preparing seasonal meals in a very traditional Kyoto style.
If you want to book for the Autumn season, you'll have to call from the 1st of May (office opens at 10pm), you'll need to book for 3 or more people, and good luck with the Japanese!