Apartments For Rent In Calumet City . 768 greenbay avenue, calumet city, il 60409. Studio apartments average $1,419 and range from $1,369 to $1,369. Garden House of River Oaks II Apartments Calumet City, IL from www.apartments.com 61 apartments rental listings are currently available. A rental apartment unit in calumet costs you from $290 to $3,095. Use our detailed filters to find the perfect place, then get in touch with the property manager.