Of the vast majority of cities in the USA that I have been to, driven through, or heard of, the wealthier sector of the population can be found in the north and west side of the city- almost without fail.
My guess of why this phenomena repeats itself all over the country is simple. In general in this part of the world rivers tend to flow from north to south and since most cities began their life around the benefits of shipping goods in and out, it made sense to put factories in the southern part of the city while building homes in the northern part. This was beneficial because the north side enjoyed cleaner water and less smog. Now as time went by and the production of goods slowed down in the cities, it was cheaper to build a house in the southern part of the city than do so in the already residentially established north side of the city.
As to why cities tend to have the west side as the wealthier side, today I learned that it seems to be due to the way winds in the USA blow, mostly from west to east. This means that if you built your house on the east side you would be stuck with industrial smog more often. But building on the west side allows you to get away from that pollution.
If anyone has other thoughts on why cities have developed this way, feel free to comment. I’m not 100% sure im accurate, but I think its a good guess.