IF you value nature over nightlife and are pretty adept at relaxing when all the conveniences of the world aren't at your fingertips, then I'd agree with the recommendations to go to Hualian.
You are right in assuming that the level of English in outlying areas, like Hualian, will be lower. That said, if the doctor was trained in the west, likely he/she will speak English or at least understand it pretty well (I have found that the speaking varies the most).
You are also correct in assuming that transportation may be an issue in Hualian (unlike in Taipei). Either rent a scooter or live close to the hospital.
Hualian, and points farther south, have much better weather than Taipei in the winter (forgot when you're coming). Plus, if in Hualian, you are so close to Taidong as well. I have traveled completely around the island twice now. In my opinion, Hualian, Taidong, and the stretch in between are, without question, the best parts of Taiwan.
"There is a benefit even in misfortune, for it is the rod with which a man can measure the loyalty of friends."
-Tirukkural 80:796 (Hindu text)