Shimonoseki City Art Museum sits in the Chōfu area, away from the busy Karato waterfront but close to temples and old samurai-town streets. Its collection and exhibitions lean toward Japanese painting, local artists, and regional cultural history, making it a quieter counterpoint to the city's seafood markets and strait views.
It is worth adding if you are already exploring Chōfu rather than making a rushed cross-town trip just for one gallery. The museum works best as part of a slower day with Kozanji Temple, the Mori residence, and the lanes that show Shimonoseki's older side.