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If you put 漫画喫茶 in google maps, it shows several places around Shinbashi station and one near Higashi Ginza station. Haven't checked whether those are the same as in Tokyo_girl's link above. As mentioned by Tokyo girl none is right next to the fish market, but they are within walking distance (less than 30 minutes if you are not extremely slow).Just to make sure, I generally don't recommend to sleep in mangakissa due to lack of comfort. You should decide whether the savings are worth it for you.

