Cheap Apartments For Rent 60639 . We found exactly 59 apartments for rent in the 60639 zip code of chicago metro, il. 4058 w armitage ave apt 3r, chicago, il 60639. 1610 N Mason Ave Apartments for Rent in Austin, Chicago, IL 60639 Zumper from www.zumper.com No matter how much (or how little) you want to spend, apartment finder. A 2 bedroom apartments averages $2,492 and ranges from $441 to $11,800. Find apartments for rent in 60639, chicago, il by comparing ratings, reviews, hd photos/videos, and floor plans at apartmentguide.com