I was nine during my first trip to Japan. Places I remember going to and loving:

Deer Park in Nara. Culture for the parents, feeding the deer for the kids.

Tokyo Tower.

Try to find out what festivals are going on at the time. I went to a midwinter festival in Kyoto with wonderful dancing and elaborate costumes that children would enjoy.

Depending on your kids' personalities, think about spending some time in a ryokan. I found it tremendous fun to run around barefoot inside, wear the too-big bathrobe, sleep on the floor, etc. Ryokan also usually serve breakfast and dinner to the family in your own room, which is a nice way to relax together.

Shows aimed at children can be very enjoyable even when there is no translation. We went to an "ice capades" type show where Japanese folk tales were performed on ice. Everything was in Japanese, but we loved it.

This trip when I was nine changed my life, making me a huge fan of all things Japanese -- a decade later I was studying the language in college. I hope your children have as wonderful an experience as I did.