The kissaten is Japan’s answer to an American diner. The essential elements are coffee, stick-to-your-ribs food and a genial, homey atmosphere. Lawn in Yotsuya is a classic kissaten, the kind of place to smoke cigarettes and scribble in a notebook. There are no laptops in sight.

Hiroaki Ogura, the owner, has been serving up orders for a half century. “We opened in Showa 29—that’s 1954,” he says. “I took over the shop 10 years later, so I’ve been doing this for over 50 years.”

Ogura is busy as he speaks, pouring coffee from a red enamel kettle with one hand, and melting butter in a pan with the other. The Beatles play on the stereo and cigarette smoke hangs in the air over the red vinyl booths. The kitchen is tiny, with a two-burner stove and just enough space for one che...