NO. The south side is huge, and has a wide variety of neighborhoods. There are some lower income areas and some middle class areas. There's not a lot of super wealthy areas. The south side is pretty working class. There aren't really any trendy neighborhoods or anything. The crime is definitely higher than on the north side though. Most people who move to Chicago from out of town do not live on the south side - they stick to the north side. But that doesn't make it dangerous. The west side has the largest problem with crime.
