Kissaten are pre-WWII style coffee shops with wood paneling, hand-dripped coffee, and Showa-era jazz. Tokyo has dozens.
Try Cafe de l'Ambre in Ginza (since 1948), Cafe Trois Bagues in Shinjuku, or Coffee Hosomichi.
Coffee is taken seriously — siphon brews and pour-over by white-jacketed masters. Expect 800–1,500 yen for a cup, with no rush.