I should have first of all posted where Philosopher’s Walk (or path) is. It is a very popular path to enjoy walking when you go to Ginkakuji-templeor Nanzenji-temple because it is a path connecting Nanzenji-temple and Ginkakuji-temple.
I strongly recommend you that you visit Ginkakuji-temple and walk through Philosopher’s path and visit Eikando-temple and walk again to Nanzenji-temple. Of course you can start from Nanzenji-temple and end your tour at Ginkakuji-temple. It is popular because of its two fascinating features. One is hundreds of cherry trees along the path and the other is the Sosui, the canal running along the path like a stream from Lake Biwa built in 1890.
You can enjoy some temples and shrines very close to the path to make a slight detour.
Best season to walk Philosopher’s Walk is when cherry trees are in full bloom, that is, in early April, however I think every season has its own attraction. I wish I could show you that.