Apartment For Rent Near Dunning Chicago Il . Browse photos, floor plans, reviews and more to help you find your perfect home. Dunning chicago apartments for rent. Best Apartments for Rent in South Side Chicago Chicago, IL RENTCafé from www.rentcafe.com Search over 4 apartments in dunning, chicago, il currently available for rent. Visit rent.com® to find your next apartment now! As of june 2022, the average apartment rent in dunning is $954 for one bedroom, and $1,102 for two bedrooms.