Your American health insurance probably covers you while you're in Japan (check your policy terms), but you would have to pay out of pocket and then claim reimbursement for whatever your policy covers. Health care costs in Japan are uniform across providers and somewhat cheaper than in the US; for example, short doctor visits (without local insurance) are likely to cost less than $100, whether you go to a small clinic or a large hospital. I used to have the standard national 70% coverage when I lived there, and typically paid $10-20 out of pocket to see a doctor.