"My doctor is from New York."
是 (shi4) doesn't mean "is" when referring to locations. You ALWAYS use 在 (zai4) when talking about where something is located. So in the sentence "My doctor is in Hong Kong/ 我的医生在香港" the verb 在 means "is in". You don't add 是 here because it's unnecessary and it doesn't make sense.
Likewise, the reason why you use 是 when saying "My doctor is from Hong Kong/我的医生是香港人" is because you're describing the doctor, not saying his location. We don't know if he is currently in Hong Kong (in which case we would use 在), but we do know that he is from there (or lit. he is a hong kong person). So, we use 是。
我的医生来自纽约。 Wǒ de yīshēng lái zì Niǔ Yuē。来自 lái zì - means to come from a place.