Setting: Japan circa 1990, a small city, sometime between 8 pm and midnight.
Hero (16yo male) is rescuing runaway Kid (9yo male) who has gotten wet, and at the moment he can't go to either of their homes or hand him off to a friendly policeman For Reasons.
If this was in the States, I'd have him check into a motel, put Kid in a hot bath, and hand-launder his clothes with the leftover shampoo and the hair-dryer, but I don't know enough about comparable lodgings and their bath amenities in Japan, and my Google searches (japan motel bath, japan lodgings bath, japan motel amenities) tend to bring up either specific --- often American --- establishments' ads or information on things I can't use, like ryokan (too upscale), capsule hotels (too tight and unprivate), and love hotels (too skeevy and windowless). What little hints I can find ("ingenious arrangements where one faucet serves tub and sink" etc) are too vague to work from.
So. The things I need are: a relatively affordable way for Hero and Kid to spend the night, a way to get Kid warm and dry (he could feasibly have a dry change of clothes on him), a suitable place for them to have a touching emotional scene, and a way for Hero to see it with a few minutes' warning when the police arrive. I initially wanted a room with a private bath and a TV, but I'm also considering having Hero take Kid to a bath house and them passing the night in a quiet-ish corner of a shopping mall or arcade (ETA: just thought of a laundromat, too) or something if that would be more practical.
I also looked up "homelessness in Japan" for ideas and found internet/manga cafes, but c. 1990 is probably too early for that.