Hagi is one of western Honshu's best historic towns, set between low mountains and the Sea of Japan. It was the castle town of the Mori clan and the Choshu domain, and it still has samurai lanes, earthen walls, merchant houses, temples, pottery kilns, and a slower rhythm than the cities on the Sanyo coast.
The town matters because Choshu mattered. Students and samurai from Hagi helped pull Japan out of the Tokugawa order and into the Meiji state, and several local sites are now part of the UNESCO-listed story of Japan's industrial revolution. Shokasonjuku Academy and Shoin Shrine is the clearest place to feel that shift from domain politics to national modernisation.
Hagi is also pleasant in a simpler way. The old Hagi Castle Town is made for wandering by bicycle, Tokoji Temple has one of the city's most atmospheric clan graveyards, and Kikugahama Beach gives the town a soft edge of sand and sea. It is not on the fastest route through Japan, but it is worth the detour if you care about the end of the samurai age.