I study how applicants to a public housing authority in the United States made choices on where to live, and what those choices reveal about their preferences over neighbourhood characteristics. I exploit an allocation mechanism used in this housing authority in which residents were given a meaningful choice about where to live. Under this mechanism, applicants are placed on a waitlist and open units are offered to applicants at the top of the waitlist. Rent does not depend on the unit assigned, housing offers are random from the point of view of the applicant, and there is variety in housing unit location and type. Applicants may reject one offer without penalty, but rejecting a second offer places them at the bottom of the waitlist, providing a differential in cost of refusal between offers. Using the universe of offers made to applicants and their accept or reject decision over a seventeen-year period, I show that relatively more marginalised applicants, especially female and Black applicants, tend to accept less desirable offers of housing, indicating that their outside options are more limited. Applicants with children, however, are more selective, perhaps indicating a stronger family and social support network for parents than for non-parents.