Starting on the north end from Ginkakuji, Philosopher's Walk is a relatively peaceful path along a historic canal that leads most of the way to Eikan-do and Nanzen-ji.
It's shady and quiet, and a small road follows along side the trail. In addition to being a nice peaceful contemplative stroll, there are a few things to see along the way.
There are some restaurants, cafes, teahouses, and shops along the way, visible from the street. I'm not sure what this is but it was the home of several cats.
The Philosopher's Path starts just south of the approach to Ginkakuji, following the canal, so it's very easy to find. It's best seen during the cherry blossom season, when the hundreds of trees that line both sides of the path and canal are in full bloom. It's about two kilometers long and ends about five minutes north of Nanzenji. The southern end to Nanzenji is fairly easy to follow, but be sure to have a good map to keep track of where the turns should be.