Japan is usually described as a "tea culture". There's tea ceremony, tea is grown here and tea is consumed in almost all situations. But, there's also a vibrant coffee culture, and Japan has had a long standing affair with coffee.
If you want a taste of the original Japanese coffee culture, head to Cafe Paulista in Ginza. This is Japan's oldest standing cafe, dating back to 1909. When it opened, Paulista used to be a place for the intellectuals of the era to mingle and two Brazilian sailors mounted guard outside.
Though not as old, Chatei Hatou also feels like time travel. This Shibuya cafe is a soothing experience, and the baristas are extremely meticulous about brewing the perfect cup, served in expensive porcelain cups. Bon cafe in Shinjuku also serves their coffee in expensive porcelain, while Kitayama is one of Japan's best hidden secrets, where they serve beans that have been aged between 1-15 years.
Starbucks came to Japan in 1996, and began transforming the coffee scene. The old-school coffeeshops (kissaten) have been on the decline ever since, but a new crop of domestic Starbucks clones has emerged to compete. You'll see names like Excelsior or Doutor all over the city.
For espresso bars, head either to Zoka or to the stores of World Barista Champion Paul Bassett. Zoka was recently awarded the title of macro-roaster of the year, and Paul Bassett paired up with a Japanese pastry champion to offer a double-winning experience. Both stores make superb latte art, and if you like the drawings on your coffee, head to Bar del Sole in Roppongi as well.
For that unmistakable coffeeshop atmosphere, head to Ben's Cafe in Takadanobaba, where the walls are full of event notices, and they host a variety of poetry readings, art exhibits and live music.