This varies by continent and by country, but Cirk is really right about North America. (Even if we count only the 48 contiguous US states, excluding the other 2, Canada, Mexico, Central America or the Caribbean)
North America has some extremely expensive areas for real estate: Manhattan, the beaches of Florida, the Bay and the Hollywood controlled areas of California. But it is also a basically empty continent. Despite many urban areas, including some behemoths like LA, overall there's a lot of room between them, which is little inhabited, and which is, because of that, a lot cheaper to live in.
When a downtown (or even semi periphery) area of a city gets gentrified, there's nothing saying that the poorer people being pushed out have to move to a bad part of the same city or metro area. They really can move to a more rural part of the same state or for that matter any other of the 48 contiguous states. This may be harder in places which are fuller (like East Asia) or the countries smaller, limiting movement (like Europe) but it's not a big issue in countries millions of square km large; and with many empty zones.
I generally oppose gentrification on grounds I'd call "cultural", but if it happens, it's not the end of the world for lower class people. Not in North America.
This matters, also, because bad weather (whichever way you define it) is not universal in North America either. The hurricane coasts of the Gulf and Atlantic give way to other weather types as you move west (or north, or even south into the deeper Caribbean, although that would be outside the US)