Residential choices and school choices are intimately connected in school systems where school admission relies on proximity rules. In countries with universal school choice systems, however, it remains an open question whether families’ residential mobility is tied to the choice of their children’s school, and with what consequences. Using administrative data on all children approaching primary-school age in Sweden, we study to what extent families’ financial and socio-economic background affects mobility between neighbourhoods and the characteristics of schools chosen by moving families. Our findings show that families do utilise the housing market as an instrument for school choice over the year preceding their firstborn child starting school. However, while families who move do ‘climb the social ladder’ by moving to neighbourhoods with more households of higher socio-economic status, their chosen schools do not appear to be of higher academic quality compared to those their children would otherwise have attended.