This paper develops a quantifiable model of public service location to investigate the relation between urban structures and public services. The State decides on a location strategy, i.e. the number, location and capacity of public facilities, while anticipating how residential density, housing prices and locational characteristics will react. The State's objective is to maximize individual utility while minimizing the sum of fixed and variable facility costs. We prove the existence of an equilibrium for any given set of facility locations; and derive the cost minimizing set of locations using a gradient method inspired by the generalized Weiszfeld method. The model remains tractable thanks to the use of stochastic shocks to commuting decisions which yield a gravity equation for commuting flows. We show that the State can strategically locate facilities to increase population density, and thus reduce commuting and facility costs. The cost minimizing strategy is defined by a bell shaped relationship between school locations and distance to the center. In a counterfactual exercise, we then show that the provision of public services under a budget constraint generates agglomeration forces important to explain urban structures; and that a tighter public budget constraint will result in higher density in core places.