We'll first visit the Garden of the Lion's Roar (belonging to the small temple Hogon'in) which was designed by a Zen priest in the 16th century. This garden is relatively little known (it figures in hardly any guidebook on Japan), but it is a delightful place for viewing the colorful fall foliage, and it is also one of my personal favorites. It is a stroll garden with borrowed scenery, and part of it is designed to symbolize some of the tenets of Buddhism.
We'll then see the garden Sogenchi of the Temple of the Heavenly Dragon, one of the famous Zen gardens in Kyoto. (Depending on time and weather, we may also enter one of the temple buildings, the abbot's quarter.) The temple was founded, and the garden designed, by the Zen priest Muso Soseki in the 14th century, in a time of upheaval, when emperor Godaigo tried to restore imperial rule, managed to overthrow the Kamakura shogunate, but was eventually forced into exile by the first Ashikaga shogun Takauji. After his death, Muso and Takauji turned a former imperial villa into a memorial temple for Godaigo. The garden, which is one of the Unesco World Cultural Heritage Sites in Kyoto, mixes traditional Heian-era elements (pond, etc.) with new influences from Zen and Chinese ink painting (stones, dry waterfall, etc.), and plays an important role in the history of Japanese garden architecture. It is considered to be the oldest garden with borrowed scenery.
If time permits, we may also walk around Arashiyama, past a bamboo grove, ancient temple gates, and a hut in which a Haiku poet used to live.