Urban park green spaces (UPGS) are a crucial element of social public resources closely related to the health and well-being of urban residents, and issues of equity have always been a focal point of concern. This study takes the downtown area of Nanchang as an example and uses more accurate point of interest (POI) and area of interest (AOI) data as analysis sources. The improved Gaussian two-step floating catchment area (G2SFCA) and spatial autocorrelation models are then used to assess the spatial and social equity in the study area, and the results of the two assessments were coupled to determine the optimization objective using the community as the smallest unit. Finally, the assessment results are combined with the k-means algorithm and particle swarm algorithm (PSO) to propose practical optimization strategies with the objectives of minimum walking distance and maximum fairness. The results indicate (1) There are significant differences in UPGS accessibility among residents with different walking distances, with the more densely populated Old Town and Honggu Tan areas having lower average accessibility and being the main areas of hidden blindness, while the fringe areas in the northern and south-western parts of the city are the main areas of visible blindness. (2) Overall, the UPGS accessibility in Nanchang City exhibits a spatial pattern of decreasing from the east, south, and west to the center. Nanchang City is in transition towards improving spatial and social equity while achieving basic regional equity. (3) There is a spatial positive correlation between socioeconomic level and UPGS accessibility, reflecting certain social inequity. (4) Based on the above research results, the UPGS layout optimization scheme was proposed, 29 new UPGS locations and regions were identified, and the overall accessibility was improved by 2.76. The research methodology and framework can be used as a tool to identify the underserved areas of UPGS and optimize the spatial and social equity of UPGS, which is in line with the current trend of urban development in the world and provides a scientific basis for urban infrastructure planning and spatial resource allocation.