Outwest Chicago Apartments For Rent . An apartment home for rent in this town costs you from $775 to $3,440. The average apartment rent in chicago is $2,080 per month so any rental south of $1,664 would be considered cheap here. West Side Chicago Apartments for Rent Chicago, IL RENTCafé from www.rentcafe.com The average home rent in this city is $3,231. Over the past month, the average rent for a studio apartment in chicago increased by 2% to $1,100. 1201 west adams street is a rental property located in chicago, il.