This paper analyzes the effects of providing environmental amenities associated with open space in a discrete-space urban model and characterizes optimal provision of open space across a metropolitan area. The discrete-space model assumes distinct neighborhoods in which developable land is homogeneous within a neighborhood but heterogeneous across neighborhoods. Open space provides environmental amenities within the neighborhood it is located and may provide amenities in other neighborhoods (amenity spillover). We solve for equilibrium under various assumptions about amenity spillover effects and transportation costs in both open-city (with in- and out-migration) and closed-city (fixed population) versions of the model. Increasing open space tends to increase equilibrium housing density and price within a neighborhood. In an open-city model, open space provision also increases housing density and price in other neighborhoods if there is an amenity spillover effect. In a closed-city model, housing density and prices in other neighborhoods can decrease if the pull of the local amenity value is stronger than the push from reduced availability of developable land.We use numerical simulation to solve for the optimal pattern of open space in two examples: a simple symmetric case and a simulation based on the Twin Cities Metropolitan Area, Minnesota, USA.With no amenity spillover, it is optimal to provide the same amount of open space in all neighborhoods regardless of transportation cost. With amenity spillover effects and relatively high transportation cost, it is optimal to provide open space in a greenbelt at the edge of the city. With low transportation cost, open space is provided throughout the city with the exception of neighborhoods on the periphery of the city, where the majority of the population lives. A greenbelt still occurs but its location is inside the city.