Both questions will give the same answer, but they are slightly different. The word "which" implies that you are deciding from a selection of cities. For example... "There are many large cities in the United States, which one do you live near?" In contrast, "What city do you live in?" is a more open ended question that implies you are relying on the person answering to provide more information.

I‘m not saying Bobby’s wrong, but I frankly don’t think very many native English speakers in the US would notice or even know what the difference is between which and what in your question. „Which“ does imply a choice of various places to pick from, and „what“ does seem to just ask the name of the City, as is „What’s the name of the place?“ True, but with these two words being so close you can really not worry about distinguishing between them. I’ve heard them both used so interchangeably that I’d not pay any attention to the difference in the exact sentence you posed.