The impact of human activities and climate change occurs across a range of spatial and temporal scales, and the city or regional scale is critical for managing food-energy-water (FEW) resources. We develop a coupled human-natural system model for Cape Town, South Africa, which consists of an agent-based model and a regional hydrologic model, to study the FEW nexus connecting the agricultural, urban, and hydroelectric generation sectors. We use the model to compare three policies—a simple adaptive approach, adaptation with free water to indigent households, and water supply augmentation—and assess their ability to provide reliable FEW services to the different stakeholders under four different climate scenarios, representing moderate to severe amounts of warming. Our results indicate that Cape Town is likely to face increasing water stress as temperatures rise, and that adaptation strategies could effectively mitigate the effects of water limitations and avoid severe failures in providing FEW services across sectors. One way to manage demand for FEW services is by adjusting water price tariffs, but high prices create inequality in access to water for households with different incomes. Our analysis suggests that the water supply system in Cape Town may already be at, if not over, its sustainable capacity within the FEW nexus. Our model serves as a test-bed for assessing policies to manage stresses on water resources for the benefit of stakeholders across FEW sectors. This model can be adapted to cities and regions around the globe.