When we were in Himeji in April we discovered that the Tourist Bureau lends bikes for free! These are standard one-speed city bikes with fenders, a bell, and lock. We borrowed ours at noon and kept them until they closed at 6pm. The Tourist office is located on the main road from the Shinkansen station to the castle -- about two blocks before the castle on the right.
It was probably the most pleasant day on our trip -- and having the bikes played a major part. The cherry blossoms were in full bloom, and the weather was fair. It was mid week so not very crowded. The best part about having the bikes was that we were able to cover more ground -- not to mention get off our sore feet! Most people were only seeing Himeji's famous castle from the front, but we were able to leisurely ride all the way around the vast grounds. We ended up riding around the park three times -- and with all the moats and walls we never went the same way twice! When we toured the castle or wanted to go into a shop, we just locked them up with the provided lock and key.
All the bikes appeared to be about the same size -- no children's bikes. That wasn't a problem for us -- our son is over 5'6" (168cm). I'm 6 feet tall (183cm) and I put the seat up all the way and it was still a bit low, but it wasn't bad. My son's bike got a flat tire (when he ran over a rock). He walked it back to the tourist office and exchanged it for another bike!
I would definitely recommend it to anyone going to Himeji.
Are there any other places in Japan where you can borrow bikes for free?