Renting a one-bedroom apartment in desirable central neighborhoods like Lincoln Park, West Town, and the Near North Side costs between $1,750 and $2,000 per month, according to apartment rental site Zumper. (Zumper also puts the average cost of a one-bedroom in Chicago at slightly higher than Zillow, at $1,670.) Single renters can save by looking for place in further-out neighborhoods like Kenwood, Rogers Park, and Irving Park, where average rents for a one-bedroom are all un