I am not sure where your figures come, but as someone who looked seriously at eight houses in various neighborhoods of Chicago, you can find quite suitable houses in the $200-250k range.
I guess I should have specified that I'm thinking of 3+ bedroom homes. Here's what Zillow looks like for a wide drawing of north-side Chicago SFHs under $250k.
This is dominated by auctions and homes in very rough west-side neighborhoods. Yes, there are a small handful of exceptions which are typically very old homes that have not been updated in decades, but to act like above $250k is "weird" or out of the norm is just not in line with reality.
http://www.zillow.com/homes/for_sale/house_type/3-_beds/0-25...
This is dominated by auctions and homes in very rough west-side neighborhoods. Yes, there are a small handful of exceptions which are typically very old homes that have not been updated in decades, but to act like above $250k is "weird" or out of the norm is just not in line with reality.