Pullman Apartments For Rent Chicago . Use our detailed filters to find the perfect place, then get in touch with the property manager. Let apartments.com help you find your perfect fit. Cougar Ridge Apartments Pullman, WA from www.apartments.com Find west pullman apartments for rent that you'll love on redfin. Find apartments for rent in west pullman, chicago, il by bedroom, cheap to luxury, pet friendly, with utilities included and more. Unique space with lots of original charm.