I've been working on a personal project that's somewhat relevant to this.

I made this map that shows where rent for a 1 bedroom apartment is $700 or less across the US, by county, with Fair Market Rent rates calculated by HUD at the 40-50th percentile. As you might expect, not a lot of the desirable places are options.

It'd be better to do it by city or by neighborhood with actual market listings, of course.