Top Knife - FL is a strong, competent head of neurosurgery department, who chose medical career over family and doesn't regret her decision. No fansubs available yet but it should be on GEM TV with English subtitles. Romance as a side story; 'family' is a more prominent theme in this one I think.
Medical Team: Lady Da Vinci no Shindan - all-female medical diagnosis team. FL does suffer from a mental disorder but it only becomes a major issue in the finale. No ML, no romance (or vaguely hinted at, I can't remember).
Doctor-X - already recced above. I strongly recommend this one as well!
Code Blue - characters have their ups and downs but they usually overcome their problems on their own. Romance only as side stories (but very good).
Good Doctor - ML is autistic. I've only seen the Japanese remake but other versions have good reviews as well.