I would advise against Berwyn. It's better than Maywood, but not a super great place to live in terms of safety, community, etc. Which is why it's probably looking like you can get "more for less" in terms of rent. I'd recommend sticking with River Forest, Forest Park, Oak Park, and Westminster (if you haven't looked into that yet!).
I would disagree with the advice against Berwyn. A community is what you make of it. Yeah, its a little more run down than River Forest, Forest Park, etc. But if you get to know your neighbors, it can be great.
This is coming from someone who lives in Pilsen, in Chicago - don't let talk of crime dissuade you from a location - nowhere in Chicago is so bad as to be unlivable, especially if you get to know the people around you - people look out for each other.