The good thing about Ryouanji 竜安寺 is that it’s right next to Kinkakuji. Well, actually 2 bus stops away, but close enough that most people are going to visit both together.
The other cool thing about Ryouanji is that it contains Japan’s best Zen garden. If you could gain enlightenment meditating at a Zen garden, then this would be the one. Unfortunately part of the place was under renovation, and half the garden was under scaffolding. There was also a lot of calligraphy on display, not sure of their significance though.