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With the growing challenge of aging populations around the world, the study of the care services for older adults is an essential initiative to accommodate the particular needs of the disadvantaged communities and promote social equity. Based on open-source data and the geographic information system (GIS), this paper quantifies and visualizes the imbalance in the spatial distribution of elderly care facilities in 14,578 neighborhoods in downtown (seven districts) Shanghai, China. Eight types of elderly care facilities were obtained from Shanghai elderly care service platform, divided into two categories according to their service scale. With the introduction of the improved Gaussian 2-step floating catchment area method, the accessibility of two category facilities was calculated. Through the global autocorrelation analysis, it is found that the accessibility of elderly care facilities has the characteristics of spatial agglomeration. Local autocorrelation analysis indicates the cold and hot spots in the accessibility agglomeration state of the two types of facilities, by which we summarized the characteristics of their spatial heterogeneity. It is found that for Category−Ⅰ, there is a large range of hot spots in Huangpu District. For Category−Ⅱ, the hot-spot and cold-spot areas show staggered distribution, and the two categories of hot spot distribution show a negative correlation. We conclude that the two categories are not evenly distributed in the urban area, which will lead to the low efficiency of resource allocation of elderly care facilities and have a negative impact on social fairness. This research offers a systematic method to study urban access to care services for older adults as well as a new perspective on improving social fairness.