You can do it either way, but the smart thing to do would be to get a 1 week JR Rail Pass (you need to get the order for it before you arrive in Japan), then activate it after your 1 week in Tokyo. Then go to Kyoto/Nara/Osaka and Hiroshima and back to Kansai Airport within the week you can use the pass.
You could spend a full day in Hiroshima and Miyajima, spend the night, and the next morning go to Kansai or if at the end of your trip to Kansai airport for your return flight. For Hiroshima City itself there is not much - just the Genbaku Dome/Peace Park, Hiroshima Castle and the Shukkeien Garden, if you like. If you find yourself with some extra time, which is possible, there is also the Mazda car museum.
It would be a tragedy if you spent 1 whole week in Tokyo though. If you haven't been out there yet, go on day trips to see Kamakura, Nikko, and the Fuji 5 Lakes. There are many regional rail passes you can get for the Tokyo area. See
http://www.jreast.co.jp/e/pass/index.html
http://www.japan-guide.com/e/e2358_002.html
For some good info on what to see in Tokyo, try:
http://www.gotokyo.org/en/index.html
http://www.jnto.go.jp/eng/location/regional/tokyo/index.html
http://www.ar.jal.com/world/en/guidetojapan/city_information/tyo/see/akasaka/
For Kyoto, see:
http://www.pref.kyoto.jp/visitkyoto/en/
http://www.kyoto.travel/