For anyone moving to Japan with children, the question arises of enrolling the children in Japanese public school or paying top dollar for private "International" schools. I feel that the choice is not just one to based on money, but also the age and/or attitude of the child.
A public elementary school is - just like in North America - free! The only cost is school supplies, lunches, milk. Pretty standard fees. Convenience is also high as there are schools every few blocks - so the walk to elementary school is bound to be 7 minutes or less. Children are pretty open to new experience, so they also make new friends quickly and pick up Japanese culture pointers naturally.
Of course, the language of instruction is Japanese. Your child, as mine did, may just sit in class utterly confused while science, math, and social studies classes go on around him/her in an unknown language. Some wards of Tokyo do provide free language instruction to foreign children - my ward actually sent a special teacher to the school two days a week to teach my daughter Japanese. (This service is also free for the first 10 weeks of instruction.) Most schools also teach English as a once or twice a week class - so your child will have one class they understand everything in! Plus, the English teacher may be willing to help your child by translating assignments on non-English class days.
Another difference is the rigidity of classroom routine. Each day has the same basic routine, and all students do the same thing at the same time. Everyone stands up, everyone sits, everyone stands in the line, everyone has bathroom break, everyone cleans, everyone eats. There is no splitting of the class into groups with each group doing different things.
For my daughter, this was the deal breaker. She was willing to wear the hat that all elementary school kids wear while walking to/from school, she liked having special shoes for in-school, she found the required P.E. cap amusing, she wrote notes to and read notes from her classmates who could write English but were too shy to speak it - but she could not handle the group actions.
As for private International schools, they use English as their language of instruction, so this makes matters easier immediately. Some schools maintain the group actions of the standard Japanese school, others adapt a more Westernized approach. The killer on these is that most schools charge tuition near a USD equivalent of $20,000 per school year. For me, price made this option impossible for me.
My daughter lasted in Japanese elementary school for about 2 1/2 months. At that point, she gave up and refused to go! I ended up trying to do some homeschooling work with her when I would get home from work.
It made for a hard life. Work for 8-9 hours while my daughter was home alone (safe for sure, enjoying hours of movies and Internet games! But somewhat starved for human contact.), then return home to do a couple hours of home teaching, then to do general household tasks.
I had to ponder the decisions of: continue to home school? force her to attend public school? move back to the US?
In the end of the thinking, I made the most difficult decision - I chose to change custodial assignments with my ex-husband. We decided that my daughter would reside with him (in the US) for school terms, and with me for summer breaks and alternate winter breaks. So, in February, she flew to Dallas TX and began attending middle school there.
Regardless of how this arrangement works, I feel I have failed somehow in my parenting.