I'm sorry to say that this sentence (using に) is not grammatically correct. に is a particle that indicates:
- Direction of movement.
- Place of existence
- Result of Change
- Object of a verb
- Source (of a verb)
- Specific time
- The Japanese equivalent of the English 'per' (as in 'three meals per day')
You can read more about the に particle at this source, but for now I will focus on why this particular usage is not grammatically correct. So let's break it down real quick.
君の -- Your
出身地 -- birthplace
に -- ? (I don't know what this could be here since it is not grammatically correct)
どこ -- where
が -- topic marker (this is another grammar mistake)
ありますか -- does it exist?
Breaking it down, we can see that 出身地 should actually be the subject of the sentence marked by は. Further, because どこ is not a topic in this sentence, but rather a place of existence, I would replace it with に, making the end result:
But this still feels clunky to me because using the existence verb ある in this case is too repetitive. The birthplace exists because you exist, so why question its existence? It would sound much more natural as:
Which is your first sentence.
So to answer your first question, the difference is that the second of your two examples is not grammatically correct, while the first one is.
The answer to your second question is simply that に and は are not interchangeable. The source I listed above (and here) shows particles that can be exchanged with に, and in what circumstances it is allowable. You will note that は is not one of them.