How does the location of affordable housing affect tenant welfare, the distribution of assistance, and broader societal objectives such as racial integration? Using administrative data on tenants of units funded by the Low-Income Housing Tax Credit (LIHTC), we first show that characteristics such as race and proxies for need vary widely across neighborhoods. Despite fixed eligibility requirements, LIHTC developments in more opportunity-rich neighborhoods house tenants who are higher income, more educated, and far less likely to be Black. To quantify the welfare implications, we build a residential choice model in which households choose from both market-rate and affordable housing options, where the latter must be rationed. While building affordable housing in higher-opportunity neighborhoods costs more, it also increases household welfare and reduces city-wide segregation. The gains in household welfare, however, accrue to more moderate-need, non-Black/Hispanic households at the expense of other households. This change in the distribution of assistance is primarily due to a ‘crowding out’ effect: households that only apply for assistance in higher-opportunity neighborhoods crowd out those willing to apply regardless of location. Finally, other policy levers—such as lowering the income limits used for means-testing—have only limited effects relative to the choice of location.