public bath in a town or city
Refers to a communal bathhouse located in an urban area, as opposed to a hot-spring resort or a private bath. Often used in contrast with 温泉 (onsen) or 銭湯 (sentō).
This town public bath is loved by the locals.
Compound of 町 (machi, 'town') and 湯 (yu, 'hot water; bath'). The reading まちゆ is a straightforward combination of the two elements.