Green infrastructure assessment in an urban context should make clear whether the problem in the vicinity of buildings concerns vegetation quality, accessibility to any relevant public green space or urban parks that foster daily activity. Such distinct problems imply separate meanings for green infrastructure planning when the distribution of extensive green areas in the periphery, neighbourhood vegetation, and amenity-rich parks in the urban fabric is unbalanced. The present article looks at Bratislava in Slovakia using five classes of values for close-neighbourhood green quality, wider-neighbourhood green quality, public green-space accessibility, urban-park accessibility, and vegetation-temperature association. The study investigates which of these green-service qualities constitutes the constraint in the vicinity of buildings, and whether Forest Index–land surface temperature connection influences interpretation of neighbourhood vegetation. The shares of ordinal classes are transformed to the service means, residual deficit, lower tail, share of high services, grid-building displacement measure, public green space/park separation measure, and heat-induced vegetation pressure. Public green-space accessibility scores the highest mean value of 0.473 in relation to buildings while urban-park accessibility receives the lowest mean value of 0.226. In turn, the share of low and very-low-value categories of urban-park accessibility constitutes the largest lower-tail proportion with 81.5%. Close-neighbourhood green quality and wider-neighbourhood green quality reveal service means of 0.358 and 0.380, respectively, together with corresponding proportions of lower tails of 64.8% and 62.6%, respectively. Forest Index possesses the mean Spearman absolute association coefficient with land surface temperature of 0.762, indicating strong association between vegetation deficit and thermal environment. In conclusion, Bratislava faces major problems concerning lack of urban park access and poor vegetation quality in the close vicinity of buildings.