Gion is the district that learned to perform and never stopped. It grew up serving Yasaka Shrine, became the city's quarter of teahouses and geiko, and still works that way behind latticed fronts — which is why the walk is mostly looking, slowly, in the right light. Do it at dusk, when the lanterns come on.
Start up Hanami-koji, the main lane of machiya (wooden townhouses) turned ochaya teahouses; the private alleys off it now carry photography bans, so keep the lens for the street. Walk east to Yasaka Shrine, the vermilion jinja the whole district answers to, its dance stage hung with lanterns after dark.
Then north to the Shirakawa, a willow-lined canal that is the quiet half of Gion — the Tatsumi bridge, the tiny shrine beside it, the unbroken townhouse run of Shinbashi-dori. End across the Kamo at Pontocho, the narrow dining alley, where a maiko (apprentice geisha) might cross at dusk between engagements. Sanjo and the Keihan line are at the top.