I recommend Meguro Dermatology Clinic (
http://meguro-derm.jp/en/) or Garden Hiroo Clinic (
http://www.gardenclinic-hiroo.com/).
I went to the latter when I thought I had an STD on my member. The doctor was female. I can't remember her name but she was amazing! Extremely professional, to the point and my 4 visits were all under 10 mins. It turned out not to be an STD, but she recommended everything for my course of action and I had a lengthy but unstressful few months, thanks to her guidance. Meguro Dermatology for general non-genital skin issues. Also fluent English speaking and really professional, though I'm not sure how they do with complex skin issues because I saw a few customers talking that they want to get a second opinion because the doctor didn't seem to know much about what they had.