With the increasing demands of urban populations, achieving a balance between the supply and demand in the spatial allocation of urban green park spaces (UGSs) is essential for effective urban planning and improving residents’ quality of life. The study of UGS supply and demand balance has become a research hotspot. However, existing studies of UGS supply and demand balance rarely simultaneously improve the supply side, demand side, and transportation methods that connect the two, nor do they conduct a comprehensive, multi-dimensional supply and demand evaluation. Therefore, this study evaluates the accessibility of UGS within Hefei’s built-up areas, focusing on age-specific demands for UGS and incorporating various travel modes, including walking, cycling, driving, and public transportation. An improved two-step floating-catchment area (2SFCA) method is applied to evaluate the accessibility of UGS in Hefei’s built-up areas. This evaluation combines assessments using the Gini coefficient, Lorenz curve, location entropy, and local spatial autocorrelation analysis, utilizing the ArcGIS 10.8 and GeoDa 2.1 platforms. Together, these methods enable a supply–demand balance analysis of UGSs to identify areas needing improvement and propose corresponding strategies. The research results indicate the following: (1) from a regional perspective, there are significant disparities in the accessibility of UGS within Hefei’s urban center, with the old city showing more imbalance than the new city. Areas with high demand and low supply are primarily concentrated in the old city, which require future improvement; (2) in terms of travel modes, higher-speed travel (such as driving) offers better and more equitable accessibility compared to slower modes (such as walking), highlighting transportation as a critical factor influencing accessibility; (3) regarding population demand, there is an overall balance in the supply of UGS, with local imbalances observed in the needs of residents across different age groups. Due to the high specific demand for UGS among older people and children, the supply and demand levels in these two age groups are more consistent. This study offers valuable insights for achieving the balanced, efficient, and sustainable development of the social benefits of UGS.