Chōfu (長府), east of Shimonoseki Station along the coastal road, is home to the old castle-town area. While little remains of the castle itself, there are earth walls and samurai gates, several temples and shrines, and inviting narrow streets, making it an atmospheric spot for a wander.
Chōfu is about 20 minutes by bus (¥370, frequent) from Shimonoseki Station. Buses run regularly along the main coastal road, stopping at Karato along the way. For Shimonoseki City Art Museum and Chōfu Garden, get off at Bijutsukan-mae; for Kōzan-ji and the castle-town area, which is what most visitors are interested in, get off at Jōkamachi-Chōfu, a couple of stops further along. Then walk back a block and turn right at the small river, following it to the end. Along the way you'll pass an always-open former samurai house. At the end, turn left to Kōzan-ji itself. After visiting its Zen-style hall and the burial plot of the Mōri lords, recharge at the adjacent Antiques & Oldies cafe, or head north a few blocks to the Chōfu Mōri Residence, which dates to 1903, for a matcha (powered green tea) and a look at its pristine garden.