At 268 meters high, Hinoyama offers good views of the Kanmon Straits. There's a ropeway to the peak if you'd prefer not to hike (¥200/400 one-way/return), and a pleasant park at the top. And since there's not enough of them in the city below, you'll find a fugu restaurant (11:00-21:00) and souvenir shop (09:00-18:00) as well. Buses run from JR Shimonoseki Station.
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赤間神宮
A shrine dedicated to the loser of the Battle of Dan-no-ura, Emperor Antoku of the Heike Clan, whose tomb is on the premises. Aside from the impressive vermilion gate, look for Hoichi Hall and the statue of Mimi nashi Hoichi (Earless Hoichi), who features in a well-known ghost story by Lafcadio Hearn.
春帆楼
The Treaty of Shimonoseki, which ended the First Sino-Japanese War, was signed on this site in 1895. There is a small museum (built in 1936) dedicated to the treaty with period furniture and some relics. It's next to an expensive ryokan (see Sleep).
旧下関英国領事館
Built in 1906, with the small Shimonoseki Ijinkan Museum inside and a tea house in the back.
旧秋田商会ビル Akita Shokai
This European-style building originally housed the offices of a shipping company. There's a particularly nice Japanese garden on the roof; the first floor has sightseeing information and a gift shop.
下関南部町郵便局
Built in 1900, this is the oldest post office still in service in Japan.
海響館
Dolphins, penguins, and sea lions join over 100 varieties of pufferfish, with four floors of exhibits about marine science and shows throughout the day. It's right next to the Kanmon Bridge, and buses run directly there.