One of the more hidden places in Kyoto is Taizoin Zen Buddhist Temple(Their English page is here). I went there in November to see the autumn leaves and I enjoyed it quite a bit.
Even though I went on a Saturday in November but I was pleasantly surprised as it wasn’t crowded. Even their Facebook page has a distinctly Zen aspect to it, complete with really nice pictures (which, in my opinion, make Taizoin look better than it really is).
It was fairly small and has several rock gardens and a pond. There is also a cafe you can have tea in and look out on the gardens. It was a bit short overall, but was a rather pleasant experience.
Unfortunately, Taizoin is actually a bit difficult to get to. While it is reasonably close to Ryoanji and Kinkakuji, there isn’t an easy way to get from one to the other outside of simply walking or taking a taxi. If you’re coming from Sanjo Keihan, take the 63, 64, or 65 buses and get off at Myoshinji mae bus stop. If you’re coming from Kyoto Station, take the number 10 bus and get off at Myoshinji Kitamon mae bus stop.
Taizoin is open from 9:00 to 5:00 (you have until 5:00 to enter), and admission costs 500 yen for adults and 300 yen for middle school and elementary school students.