Care facilities are the mainstay of social services for the elderly. As the trend of empty nesting among elderly families intensifies due to the aging population, it is becoming difficult for families to take on the responsibility of caring for the elderly on their own, and the elderly need more formal care to be provided by society. The contradiction between the lag in the construction of care facilities and the growth in the social demand for elderly care has been highlighted, and the spatial equality of care facilities is an important means of achieving an optimal allocation of resources for elderly care. In this paper, we use the two-step floating catchment method to measure the spatial accessibility of care facilities from a fine-grained perspective, using big data, including mobile phone signaling data and points of interest. Then, we use the Gini coefficient to analyze the equality of the spatial allocations of different types of urban care facilities. The results of the study show that, first, the spatial equality of care facilities is good in terms of the Gini coefficient, but the overall spatial accessibility of care facilities is at a relatively low level compared to that in developed cities. This means that the layout of Changchun’s care facilities is good, but there is insufficient service capacity. Second, the spatial accessibility of residential care facilities is characterized by a gradual decline, with high levels in the core and low levels in the periphery. Fewer facilities are located in the peripheral areas of the city, and spatial accessibility is at a lower level, a characteristic different from that seen in cities with a higher level of economic development, such as Beijing. Third, the spatial accessibility of community care facilities showed a polycentric, contiguous distribution. The effect of the study scale on the spatial accessibility of community care facilities was more pronounced, with large scales obscuring the high values of the spatial accessibility of community care facilities in peripheral areas. Fourth, Changchun has better overall equality of care facilities, with differences in the different types and areas of care provided. The spatial balance of care facilities in the core area is better than that observed in other regions. In conclusion, this paper underscores the value of big data, such as mobile phone signaling data, in supporting refined urban research. Furthermore, our comprehensive analysis of social care facility equality can inform policy making and spatial planning.