This post covers the area north of the Gion area / Higashiyama station.
If you get off at Higashiyama and continue following the streat to the east you will cross a street which directly leads to the Heian Shrine. You will not miss that street since a gigantic big Tori gate welcomes your entrance. The shrine is freely accessible with a seperate paid garden area. Sitenote: it was quite hard to find any bicycle parking lots.
The Higashi Tenno, or Okazaki Jinja, is a very small shrine featuring rabbit statues. Rabbits are said to have been the messenger of the shrined god but through the years the symbolic meaning of the shrine changed and now the rabbits, who are known for great production of offsprings, stand for success with conceiving and a safe birth. No wonder at the time of our visit we saw a lot of women (japan-visitor.com, 13.10.2019).
The Konkai Komyo-Ji is a shrine complex with quite a beautiful garden area. You can get quite a nice city view on top of the hill next to the Pagoda.
The Philosophers Path is a approximately 1.8 km road along the Lake Biwa canal leading to the Ginkaku-Ji. It is actually chosen for the 100 Best Japanese Roads and indeed it is a pleasent walk among trees and a paved road.
Contrary to its name Ginkaku-Ji, the silver pavillon, this pavillion is actually brownish. It comparison to other “garden” areas in Tokyo this one is rather small nonetheless well maintained. There is a straight path which you can follow to see the garden architecture modeled after natural landscapes. In combination with the Philosophers path it does provide a good afternoon activity. The entrance fee is 600 Yen.
This more remotely located park is around the same size as the Yoyogi park in Tokyo however it doesn’t has as much open space. The area is devided by trees and features quiet a big lake.