Should I simply try to launch in my local city and see if my business model works first?
So, I would always recommend launching locally as a test. Gather data, do customer interviews, watch people using it in real life, and so forth. Then regroup and digest what you've learned, iterate your product based on that, and follow up with a larger scale launch.
There are many other unknowns launching in a city you are entirely unfamiliar with, especially if you have to move there.
It comes back to what the app actually does. Do you have to be in the city to launch it? Is there an offline component of it? If the answer is yes, stay home.