JKT,
Hiroshima is quite a nice city as far as cities go, but its main attraction for tourists is the A-bomb museum and Peace Park. As I say, worth seeing the museum at least once just to be aware of the devastation the bomb caused. And to think that was only a 12 kiloton bomb (13-16 according to Wikipedia), compared to the multi-megaton ones they have now! In the end though, it depends on what you're really interested in seeing. Remember it's your holiday, not ours. Don't go if you would really prefer to go somewhere else. There's probably nothing there you won't be able to look up on the Internet, but there is something about being there...
Miyajima is scenic, but like most scenic outdoor places, it's 100 times better on a nice day. Nara is also fine-day material, as you spend most of the day outdoors and it wouldn't be terribly pleasant in the rain. Ditto Nikko.
You could potentially visit Hiroshima and Miyajima on the same day, if you made it a long one and didn't waste any time, but it would be much more comfortable as two days. I think you could do Himeji and Hiroshima as half a day each though, if all you wanted to do in Hiroshima was see the museum and Peace Park. Likewise Himeji and Koraku-en garden. Depends a bit though on how mobile you are (ie. do you mind a fair bit of walking and early starts, or do you prefer to sleep in and just dawdle).
Regarding accommodation, I gather Kyoto has quite a lot of it, but you want something conveniently located. If you're only there for the market and perhaps a temple or two, then you could stay somewhere near those places, but if you intend to use it as a base for other places as well, then you might prefer to be near the station.
However, as I mentioned, you could day-trip there from somewhere else. Don't under-estimate how far you can travel on the shinkansen for a day trip (with a rail pass). According to Hyperdia, Okayama to Kyoto is less than 1.5 hours, so even a day trip from Okayama is feasible. We travelled up to 2.5 hours each way for some day trips.
Another advantage of staying in less places and day tripping is that you can be more flexible with where you go each day, and even change plans completely. Since some places are much better on fine days, head to say Nara and Miyajima on fine days, then if it rains, you can go to Hiroshima, Osaka, or Himeji (Himeji would be better on a fine day too of course, but if I had to choose, I'd pick Himeji for a wet day over Nara or Miyajima).
Finally, with regard to taking the shinkansen, if you have a rail pass you cannot use the Nozomi trains. Of the other two, the Hikari and Kodama, the Hikari are the express trains, and the ones you want for trips of any length. From the 2006 trip, I remember the Hikari's often only ran once an hour along that line, so get a timetable and be aware of what time those trains run if you want to avoid wasting time. Carry the timetable with you on days when you need to get the train back again. Try to turn up 10-15 minutes early and find the right queue for a non-reserved non-smoking carriage (a bit tricky until you get the hang of it). If you arrive right on time for a busy train, you might have to stand for some, or possibly even all, of the trip. Those trains can be very long too, and a "quick dash" to the other end might take a lot longer than you think. You might be able to get a timetable from JNTO here, but ask for the latest one (in English) from the information office at one of the major railway stations.
Good luck!
Cheers,
GP