How's your stay in China? Let me know when you (get/come/are) back to Vancouver.

*Here are two questions:
- What is the difference between get, come and are in the sentence above?
- And does this sentence sound natural?
聼起來自然嗎?

Note first that with "are" you should use "in Vancouver" instead of "to Vancouver." Moreover you can use it interchangeably with "get back to" and "come back to."

The only nuance that using "come back to" has that the other two don't is that it implies that you, the speaker, are also currently in Vancouver. If I were in Vancouver, then, I would be more likely to say "Let me know when you come back to Vancouver" or "Let me know when you are back in Vancouver."