Although it may be hard to find at first, located in the basement, Kanda Brazil is a popular cafe with locals looking for a place to work or chat with friends. The coffee is exquisite and the desserts too are all very delicious. The cafe also has both smoking and non smoking seats so you can enjoy the retro wooden interior and atmosphere either way.
Above: The coffee at Kanda Brazil is sourced from many countries, including the eponymous Brazil.
An Exchange Student's Guide to Tokyo Cafes 