Hagi Castle Town is the heart of the visit: a walkable district of white walls, old samurai residences, merchant houses, narrow lanes, and bends designed to slow attackers. It is quiet rather than polished, which is exactly why it works.
The district is part of the UNESCO-listed Sites of Japan's Meiji Industrial Revolution because Hagi's feudal order and Choshu politics fed directly into the country's rapid modernisation. Wander first, then read the history; the streets make more sense once you have seen them at walking speed.