Hiroshima Airport (IATA: HIJ) fields a fairly good selection of domestic flights as well as some from Seoul, Bangkok and various points in China. Flight time from Tokyo, the busiest route, is around 90 minutes.
The Sanyo Shinkansen from Osaka to Fukuoka (Hakata) runs down the coast of Hiroshima prefecture, stopping at all major cities including Hiroshima and Onomichi. Direct Nozomi trains from Tokyo take about four hours to reach Hiroshima and cost ¥18,500 one-way.
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