If in your mind’s eye of Japan, you see old wooden structures lining narrow lanes and paper lanterns then Kyoto is probably the best place to find this. And specifically, the Kawaramachi and Gion areas in central Kyoto are great places to soak up the atmosphere of old Kyoto. I think the evenings are the best time to walk around and especially in the summer when the restaurants along Pontocho-dori expand out over the river.
My first trip to Kyoto, I stayed south of Gion so I started...