I would avoid Woodlawn and all the areas around Midway. A friend of mine lives right by Midway and he has had his car broken into at least three times in the last month! Englewood, Archer Heights and Clearing should all be avoided.
There are gangs pretty much everywhere except affluent neighborhoods. I don't mean they're running around on the streets everywhere, I just mean they definitely exist. It's not really a problem except in the neighborhoods listed as "worst."