The Willows Apartments Austin . Find your new home at the willows located at 600 s 1st st, austin, tx 78704. Texas state affordable housing corporation 1 the willows apartments 1332 lamar square dr., austin, texas 78704 owner: The Willows Apartments Apartments Austin, TX from www.apartments.com This apartment lists for $1424/mo, and includes 1 beds, 1 baths, and 572 sq. Consider the apartments at the willows in austin, tx if you're searching for a new place to call home. Call to learn more or schedule a visit of the apartments at 1332 lamar square dr in austin, tx today.