This problem solves itself. Poor people move to cities because of limited economic opportunity where they live. You can make more money, but the cost of living rises in proportion. If you make 28K no matter where you live, then it makes sense for a lot of people to optimize by staying in or moving to places with a low cost of living. Maybe a lot of them will watch TV all day, but at least they'll be fixing up an old house so they have a decent place to live, and contributing to their community.
You absolutely don't give people more money who live in more expensive areas. Actually, by allowing people who don't really want to live in the Bay Area to move someplace cheaper and simultaneously increase their standard of living, you'd actually end up reducing price pressure in overheated real estate markets like SF, and propping it up in super-cheap areas like Detroit.