There's an old-fashioned two story coffee house place adjacent to (and even sort of part of) Piss Alley, right next to Shinjuku station I forgot the name of the place but it would definitely meet the requirement.

Exit JR Shinjuku station from the west exit, go upstairs to street level and turn right upon exit. Walk about 200m and turn right at a sidewalk just past Uniqlo. You'll see the place on the left in about 20m.