Hello Andrew, if you say your area, its easier to find something!
but here are some recommendations of clinics that have english-speaking doctors, Physicians, etc and are very foreigner friendly:
Tokyo Medical and Surgical Clinic http://tmsc.jp/
American Clinic Tokyo http://www.
Hiroo International Clinic http://www.hiroo-ic.
Roppongi Hills Clinic http://www.66clinic.
Tokyo Midtown Clinic http://tokyomidtown-mc.
The King Clinic http://thekingclinic.
Shinagawa East Medical Clinic http://www.e-clinic.gr.
We've just moved to Tokyo this month. And now I'm looking for a English speaking doctor's clinic because my kids are due to have their jabs soon. Any recommendations?