Edit 05/2019:
Zhongxiao Xingfu - my previous recommendation - has permanently closed, but I've been referred to Dr. Hsieh at this address:
3F #311 Zhongxiao East Road Section 4
台北市忠孝東路四段311號3樓
(02) 2772-8300
Dr. Hsieh is efficient and no-nonsense, speaks good English and I felt like I could trust her. I've only visited her once but that's enough for me to recommend her here.
The clinic is small but clean, and is near MRT Sun Yat-sen Memorial Hall. I was able to see her quickly, barely having to wait even though it was around 5pm (which is often a busy time). She was able to pull up my old file from Zhongxiao Xingfu and helped me exactly as I needed without my having to explain too much, including giving me choices and a recommendations.
I appreciated especially that when I said I didn't have kids, she did not ask me "why not?" (I'd been asked that before, before Dr. Wang) or assume I was planning to have them. She just took that information with no comment, which is perfect.