Kintai-kyo
Originally, the arches of this long, magnificent bridge could only be crossed by samurai. These days, the river it spans has been reduced to a trickle, and anyone willing to fork over the admission can go back and forth as they please. The 210m original was built in 1673 using only wood — no metal nails — but the present structure is a 1953 reconstruction.
Iwakuni Castle
Although the original castle only stood for seven years, that was excuse enough for a reconstruction during the 1960s. The foundations of the original lie a short distance behind the new one; the builders apparently decided to move it closer to the cliff for scenic purposes. It's about a five-minute walk from the cable-car station on Shiro-yama. Inside the castle is a small historical museum 9AM-4:30PM, ¥260.
White Snake Museum
Dedicated to exactly that: the white snakes that are native to the Iwakuni area. Not the hair metal band. As they are messengers of Benten, the Japanese goddess of wealth, an encounter with the white snakes is considered good luck.
A cable-car takes visitors up Shiro-yama to the castle. It's ¥540 for a return trip, but a combination ticket can be purchased at the foot of the bridge for admission to Kintai-kyo, the ropeway, and the museum inside the castle for ¥840. The top of Shiro-yama is a nature preserve, so it's worth a short hike after you're done with the castle.
There are two museums in the park for visitors interested in samurai culture and feudal Iwakuni. The Choko-kan Tu-Su 9AM-5PM, free is a library with historical documents and scroll paintings; the Kikkawa Museum Th-Tu 9AM-5PM, ¥500 is dedicated to the aforementioned family of warlords, and includes some of their weapons.
Kikko Park
A pleasant green spot on the other side of the bridge, with some lovely flower gardens, large sprinklers for a soak on a summer day, and a popular cherry blossom viewing spot in April. Expect to meet some chatty locals here. The entrance to the park is overseen by a statue of Hiroyoshi Kikkawa, the feudal lord who directed the construction of the Kintai-kyo; the park was built on the grounds of the Kikkawa family home.
Iwakuni Art Museum
Art and artifacts about samurai life, including some remarkable sword exhibits. The admission is a bit steep, but you'll find better English information here than elsewhere.
At the south end of the park, you'll see the dramatic Nagaya Gate of the home of the Kagawa family, who were the Kikkawa's principal samurai retainers. Also near the park is the Mekata Residence, the home of another family of Kikkawa retainers. Don't try to enter either, though; they're still private residences.