You will find below a list of a few hospital in Tokyo with English speaker available.
It is an non exhaustive list with english speaker doctor and taking the Japanese medical insurance.
Sanno Hospital in Aoyama
St Luke’ s International Hospital in Ginza
IUHW Mita Hospital in Azabu
Kitahara International Hospital in Hachioji
NTT Medical center in Shinagawa
National Center Hospital in Shinjuku
Please check the expatguide website for more information about specifics hospital or clinics.