In the US, there seems to be a slight majority of big cities where the poor side of town is to the south. A few theories have been put forward, but none are terribly convincing. The prevailing winds for most US cities are from the northwest, so areas south and east end up downwind of polluting industry. For new cities in the Great Plains and West, railroads ran east and west, so the location of the tracks and the station may have influenced what area became "downtown" and what area became "the wrong side of the tracks."

In 1939, Homer Hoyt published this look at the phenomenon, (see page 77 for the main diagram) but the main thing he took away from it was what urban geographers call the sector theory for describing urban areas.

I can give an answer in at least one example. Chicago was historically one of the largest destinations for African-Americans during the Great Migration. Within Chicago, the South Side was the largest destination - indeed, at one point, 78% of African-Americans in the city lived in a narrow band of the South Side called the Black Belt. The reason for this is that many of them came into Chicago on the Illinois Central Railroad, which was the main route into the city from the South (particularly Mississippi). The railroad's main station was located on Roosevelt Road, then (as now) a border between the Loop (downtown), and the residential areas on the South Side south of there. Arriving African-Americans looked for housing near the station, driving the concentration of them on the south side.

It's worth noting also that employment with the railroads, whether as a porter or as a redcap (station attendant), was one of the few decent-paying jobs open to African-Americans at the time. With the IC being based in Chicago, many of the African-American workers were based there and lived in this same Black Belt. Since they were likely the first Chicago residents an immigrant would encounter (and ask for housing advice), they would have further guaranteed migration to the same neighborhoods.

Sources:

Robert M. Lombardo. "The Black Mafia: African-American Organized Crime in Chicago 1890-1960". Crime, Law & Social Change 38, 2002.

James Grossman. "Great Migration". The Encyclopedia of Chicago, 2004.

Christopher Manning. "African Americans". The Encyclopedia of Chicago, 2004.

Isabelle Wilkerson. The Warmth of Other Suns: The Epic Story of America's Great Migration. <-- This is a FANTASTIC book to read if you're curious to know more.