Time Out says
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Coffee shops in Tokyo tend to open late (usually after 10am) and close early, which kind of defeats the point of caffeine – to help wake you up in the morning, or to help keep you awake at night. But coming to the rescue is Unir, where you can get your caffeine fix any time of the day or night. Located on the first floor of the fittingly titled Hotel Innsomnia Akasaka, this smart, slick speciality coffee haunt offers espresso, French press brews, granola and excellent pastries.