International Schools would only be concentrated around major urban areas. Best to place yourself in either Kanto or the Kansai area.
The British Schools are the first ones to come to mind. There are other International Schools for Germans and other nationalities as well, but unless you can speak this language, you can forget about it.
See below some schools I would recommend:
Gaining a teaching job at an International School is not easy. Most often, recruiting is done via introductions and word of mouth. If you see a job ad for an International School, it will more than likely be for a position starting in 6 months of so.
The best would be to email your resume with a DEFINITE arrival month. Then follow-up with a phone call a few days later if no reply received.