A Stroll Down the Back Streets in Higashiyama, Kyoto
Kiyomizu-dera, because from the temple it's a mostly downhill walk. You can follow the main path to Maruyama Park, or branch off and explore some side streets as well. Depending on how much browsing in stores and exploring you do, the two-kilometer walk can take one to two hours or more. Generally, shops open around 9:00 or 10:00 and close around 17:00 or 18:00.
From Maruyama Park, you can head downhill into Yasaka Shrine and the Gion district or continue north to the larger Chionin and Shorenin temples. I managed to make a full day in this area, including Gion and the temples north to Higashiyama Station, but it involved a lot of walking. If you want a really good hike, start at Kiyomizu-dera and walk past Shorenin to Heian Shrine, Nanzen-ji, the Philosopher Path, and finally arrive at Ginkakuji. This is over 3.5 miles (about 6 km), and takes over an hour to walk without stopping anywhere.