Southern Higashiyama is the most walked hillside in Kyoto, and it earns it. The trick is the order and the hour: start at the top with Kiyomizu-dera before the slopes below it wake up, then let gravity and the old stone steps carry you down through the preserved lanes toward Gion.
Three kilometres, best early. Kiyomizu-dera hangs its main hall on a forest of cypress pillars, a terrace thrown out over the hill with the city laid out beyond — go at opening and you may have the rail to yourself. Below it, the Otowa falls give the temple its name; watch the cups if you don't fancy the queue. Then down Sannenzaka and Ninenzaka, the three- and two-year slopes, machiya (wooden townhouses) turned teahouses on either side, worn stone underfoot.
Halfway down, the Hokan-ji pagoda rises clear above the tiled roofs — the one shape this quarter is built around. End at Kodai-ji, Hideyoshi's widow's quiet Zen temple, then drop to Gion-Shijo and the Keihan line.