Population aging is changing the way elderly care services are planned. This paper takes the districts and county-level areas of Dalian as the study units. It distinguishes two common service scenarios: nearby daily life support and medium-distance institutional care with integrated medical–elderly care services. The study combines transport accessibility, the spatial dispersion of the older population, and service supply intensity. Based on these indicators, it builds a supply intensity–accessibility risk framework to identify service deficits and governance priorities. The results show a clear spatial differentiation in elderly care service accessibility in Dalian. The main urban area has a lower accessibility risk, while outer districts and county-level areas face a higher risk. Shahekou District, Zhongshan District, and Xigang District show relatively strong supply and low risk in both service scenarios. Their elderly care resources are more likely to be converted into an effective supply. Pulandian District, Wafangdian City, and Zhuanghe City face both insufficient supply and limited accessibility. These areas should be the key targets for systematic improvement. Different areas also show different dominant constraints. Jinzhou District and Lüshunkou District are mainly constrained by gaps in institutional care and integrated medical–elderly care services. Changhai County is affected by its island spatial structure, so it needs stronger daily life support and transfer services. Ganjingzi District has a more specific shortage in nearby daily life support services. Elderly care governance, therefore, needs to match service type, spatial accessibility, and supply–demand mismatch. This approach can support more precise area-based allocation of elderly care resources.