Budget
Via Inn
A decent business hotel with small, pleasant rooms and Internet access, outside the east exit of the station.
Nishi Washington Hotel Plaza
Clean, Western-style rooms in a business hotel outside the west exit of the station, with Internet access and a shabu shabu restaurant on the premises.
Hinoyama Youth Hostel
Dorm rooms with tatami floors, a washer & dryer, and free Internet access. By bus, exit at the Mimosusogawa stop after passing the Kanmon Bridge and head uphill.
Midrange
Tokyu Inn
Nine floors of standard-issue Western-style rooms and a buffet breakfast. Rental PCs are available for ¥1000/night.
Shimonoseki Grand Hotel
A luxury hotel in the Karato area. Most rooms have balconies, and there's a beer garden on the roof.
Shimonoseki Marine Hotel
A bit of extra value for being a bit out of the way, in the Chofu area. Nice Japanese-style rooms and a few Japanese/Western hybrids, and good kaiseki dinners. It's next to the Marine Hot Spring Park, and combined admission is available.
There are more plentiful accommodations over the water in Fukuoka.
Shunpanro Hotel
Aside from the historic significance described above, the restaurant of this luxury ryokan was also the first licensed to serve fugu after the ban was lifted.