How does the location of affordable housing affect the distribution of assistance, tenant welfare, and segregation? Using administrative data, we first show that, despite fixed eligibility requirements, developments in higher-opportunity neighborhoods disproportionately house tenants who are higher-income, less likely to have children, and far less likely to be Black or Hispanic. We then build a structural model in which households choose from both market-rate and affordable housing options, where the latter must be rationed. For existing developments, the targeting of assistance is driven mainly by which eligible households apply, with developer screening playing a smaller role. Simulating new developments across neighborhoods, we find that building in higher-opportunity locations raises aggregate tenant welfare and reduces segregation, but primarily benefits more moderate-need and white households at the expense of higher-need and minority households. Policy levers available after construction, such as lowering income limits, have more limited effects than the initial choice of location.