[Lonthego]

I would actually have to recommend against Himeji, there is currently major construction going on right now and the entire castle is encased in a giant scaffold until like 2014 or something.

If you like history and culture though, consider
Asakusa (Tokyo)
Kamakura (Kanagawa prefecture, near Yokohama)
Kyoto (Kinkakuji, Ginkakuji, Kiyomizudera, Philosopher's Path, Arashiyama, etc.)
Nara
Uji (like 20 minutes from Kyoto in the same direction as Nara)

Probably not time to do all of it, you could spend 5 days in Kyoto alone seeing all that stuff, but it will make for a fun trip. Definitely get the JR Rail Pass by the way it's awesome.