With numerous aging societies worldwide, the world is facing a rapidly growing and already large elderly population. Elderly care facilities have become an important topic. Hence, it is urgent to examine the layouts of public elderly care service facilities, conduct rational planning, and promote the efficient utilization of facility resources. By constructing a Service Demand Equality-Frame Model and performing visualizations based on Geographic Information Systems (GISs), we assessed the degrees of spatial equilibrium between the service capacities of public elderly care services and the demand for them. The spatial accessibility and equality of hospitals, communities, and elderly care facilities in Guangzhou’s four main urban districts (Yuexiu, Liwan, Haizhu, and Tianhe) were subjected to scientific evaluation. The results have validated the effectiveness of the econometric model. According to GIS-based visualization, the spatial accessibility distributions of these public facilities are uneven with large gaps between subdistricts. Accessibility peaked in Yuexiu but gradually declined from the city center and Yuexiu to the surrounding areas. We investigated the best quantitative approaches for measuring the spatial accessibility distributions of public facilities such as hospitals and communities to improve spatial layout monitoring and optimization of elderly care facilities.