How does the location of affordable housing affect tenant welfare, the distribution of assistance, and broader social objectives such as racial and economic integration? Using administrative data on households living in units funded by the Low-Income Housing Tax Credit (LIHTC), we first show that tenant characteristics such as income, race, education, and family structure vary widely across neighborhoods, despite common eligibility thresholds. To quantify the welfare implications, we develop and estimate a residential choice model in which households choose from both market-rate and affordable housing options, where the latter are priced below-market and must be rationed. Moving a new development to a neighborhood with less poverty and better access to good schools and jobs increases aggregate tenant welfare and reduces both racial and economic segregation. However, it is also more costly to provide and disproportionately benefits more moderate-need, non-Black/Hispanic households. This change in the distribution of assistance arises in part because of the rationing process: households that only apply for assistance in opportunity-rich neighborhoods crowd out other households willing to apply anywhere. Relative to the choice of where to build, policy levers available post-construction — such as lowering the eligibility thresholds — have only limited effects on outcomes.