The urban green public spaces “UGSs” provide a place for everyday contact with nature to humans. Green and blue infrastructure is important for urban heat mitigation. This study focuses on the relationship between satisfaction with the place of living and quality of life indexes, accessibility, and the quality of public green spaces in one of the suburbs of Gdańsk in Poland. Even though there are award-winning public parks and a large-scale Tri-city Landscape Park, the individual indexes measuring the satisfaction of local inhabitants with accessibility to public parks and their quality were well beyond the average in Gdańsk. The research question was to explain such low satisfaction with green public parks and spaces in Gdańsk-Osowa. The results of the evaluation of available “UGSs” against the universal standard for health-promoting urban places confirmed their recreational value but also demonstrated limited spatial and physical accessibility and possible overcrowding. Thus, the possibilities for everyday contact with nature for numerous inhabitants are limited and that condition may influence the life quality indexes. The results suggest that increasing urban density and the further development of residential neighborhoods requires careful planning of new public parks in consideration of proximity to public open green spaces. The accessibility of public parks within walking distance is crucial when planning new developments.