Built in 794 by the Emperor at that time, in an effort to free the former capital of Nara (the very first) from an excessive influence of  buddhism, Kyoto - as its old name Heian-kyo indicates - is a capital of peace and serenity. Despite the urbanization generated by modern times, its religious past remains carved into buildings and ladscapes, and Kyoto deserves its status of exceptional city. 
Nowadays, this former capital houses around 20% of Japan national treasure, and 20 sites are part of UNESCO's World Heritage. Wherever you go, you will find a reminder of japanese culture and/or tradition.
West of the city: take a stroll in the bamboo groves or climb the hill hosting japanese monkeys, at Arashiyama. Down South, walk through the countless red torii gates of the famous fox sanctuary: Fushimi Inari Taisha. Contemplate the bright color of Ginkakuji zen temple (Silver pavillon) in the East, as well as the color of its model in North: Kinkakuji temple (Gold pavillon). In the heart of Kyoto, jump back in time and, with a bit of luck, cross paths with a geisha in a hurry.