Apartments For Rent In Alsip Il Zillow . Search 2 pet friendly apartments for rent in alsip, illinois. Located in the village of alsip, nearby public. 12020 S Kildare Ave, Alsip, IL 60803 Apartments Alsip, IL from www.apartments.com In addition, there is 1 house for rent in alsip, il 60803 with a rental rate of $466. There are currently 9 apartments. Last updated may 14 at 1:50 am.