院 institution

for once the onyomi actually SOUNDS like the English keyword! INnnnnnnnnstitution!

IN our town, we have completed our IN-stitutions = we have a library, a town hall and a university.

hospital ★★★★☆
病 (sick kanji) + 院 (institution) = 病院 (hospital)

beauty salon. ★★☆☆☆
美 (beauty) + 容 (appearance) + 院 (institution) = 美容院 (beauty salon.)

beauty salon. Yes, hospital （びょういん） and beauty salon (びよういん） DO sound totally alike.This is one of the basic mindfucks that teachers like to spring on newbies, so act like you know.