Lots of information on the web about the Philosopher's Walk.
This map shows several bus/train routes from Kyoto Station to the northern end of the Philosopher's Walk, distance about 8km (5 miles).
You need a bus going near to Ginkakuji, also named Jishoji (-ji = temple), which you may also have time to inspect. Fare from downtown Yen 240. Enter the back of buses in Kyoto, exit at the front where there are two machines beside the driver: one for changing coin or notes (at least Y1000 notes, perhaps more), the other for deposit of exact fare, no change given.
The Kyoto subway system is not to be compared with Tokyo's system. The buses are excellent.
All of our time in Kyoto was spent in the area of this map.
Some photos and story
From Kyoto Station we had to find our hotel which was small (30 rooms) and very new, not visible on street view google, or not to us. Just south of Sanjodori [Sanjo Street] on Kawaramachidori. Great location. We took a local subway trip, two stops to Shinjo and walked a kilometre and a half.
Always choose the minor streets.
before diving into the Nishiki Markets on Hajiyacho street
I steal from next day for breakfast we bought in this market, wonderful.
from this fish shop.
Leaving our bags at the hotel we set off by #5 bus for the Philosopher's Walk. No doubt a pleasant wander at other times, stunning during the cherry blossom time. This is 11 April 2014, other years may vary.
Movie of Philosopher's Walk embedded at the top of this entry