Gion

If you have a mental image from pop culture of a Kyoto neighborhood: that's Gion.  Despite ongoing city-wide modernization, great effort has been put in to preserve its historical value.  Take a stroll through and enjoy the architecture but be mindful of photography restricted zones on residential streets.  If you are interested in taking photos, Minamiza (Kabuki theater) and Yasaka shrine still offer plenty of chances - even at night.

Since Gion is home to the five hanamachi (geisha/maiko districts), you might spot a maiko headed to her next appointment if you are very lucky.  And even if you miss your chance... photography is restricted, so who is to say that you didn't?

There's always something seasonal to do in the area.  Chime in the New Year at Chion-in, see cherry blossoms at Kiyomizu Temple, cool off by the Kamo river after checking out a summer festival at Yasaka shrine and see the red leaves reflected in a pond at Kodai Temple.