Well, I lived in Japan for six years, and I've just come back from working and travelling there for two months in the summer, and I agree with Dave. All of those cities are on the standard tourist trail (both foreign and domestic), and have plenty to see and do while visiting. I can't really comment on Nikko or Hakone, but personally I found Osaka and Kobe to be boring (as a tourist). Great cities to live in, but not really much to capture your imagination. I lived in Hiroshima for two years and would definitely recommend going to Miyajima. Don't just do it in half a day, like most people. Explore the island -- it's not that big and there's lots to see besides the shrine. Stay late -- the ferries run until at least 10 or 11 p.m. and you'll get a much different feel for the island (and the lit-up Torii gate) than during the day. They have a pretty interesting fire festival that takes place on New Years Eve, if you're still there around that time.
I love and hate Kyoto. It's way overrated as a city -- it looks pretty much like every other concrete-based city in Japan -- but it does have some fantastic temples and shrines and gardens. There's one place I went that is near the beaten track, but just enough off of it that nobody goes there. Great for photography. I'll have to let you know more about it later, when I'm at home and have the proper information. Nara is worth more than a day trip, if you have the time.
If you have access to a car, I would really recommend the Sea of Japan coast, especially in the Chugoku area (Tottori, Shimane, Yamaguchi). The sea is beautiful and you can find some of classic, traditional landscapes that are missing in most of Japan due to poor urban planning and cedar forests. Similarly, going as far north or south as you can would give you some great experiences, although once you get past early November the weather and landscapes can be pretty blah until spring arrives.
If you can, try to get to as many festivals or other events as you can. Early November has shichi-go-san day (seven-five-three) when children are dressed in their first kimonos and taken to shrines or temples to pray. I've never taken photographs on that day because I always seemed to be working, but you could get a nice slice of an old custom still going strong today.
Anyway, these are just a few ideas for the moment. If you have more specific questions I can try to answer them here or via pm.