A little ways south of Hiroshima is the town of Iwakuni. It sits at the mouth of Nishiki river and on its delta. Following that river in-stream just a little ways, you come to Kintai-kyo (Kintai Bridge).
Iwakuni's bridge and castle can be reached by bus from Iwakuni Station. The bus costs 240 yen and the trip takes about 20 minutes, with buses leaving very often. The train from Hiroshima to Iwakuni takes a bit under an hour and is 740 yen. You can take the Shinkansen (kodama trains only) to Shin-Iwakuni for twice the price, but the trip takes only 15 minutes (buses from Shin-Iwakuni cost 280 yen and take about 15 minutes, but come only every 20 minutes). A combination ticket for the bridge, ropeway, and castle will cost 930 yen. The castle is open daily from 9-4:45 (closed the last two weeks of December).