We present the first dynamic model of neighbourhood and school choice to illustrate how the design of school priorities - how the school allocates places if over-subscribed - affects sorting into schools and neighbourhoods. Our model shows not only how the design of school choice affects local house prices and school composition, but also the composition of neighbourhoods in household age and completed fertility size. We focus on the comparison of over-subscription priorities between random allocation and catchment areas that give priority to local pupils. We calibrate our model to a city in England, where stylised facts match the key predictions of our model. We find that allocating places by lottery if over-subscribed increases the probability of attending the “Good” school from outside the catchment area, decrease local house prices in this area, while increasing the mixing between household types.