Disparity in spatial accessibility is strongly associated with growing inequalities among urban communities. Since improving levels of accessibility for certain communities can provide them with upward social mobility and address social exclusion and inequalities in cities, it is important to understand the nature and distribution of spatial accessibility among urban communities. To support decision-makers in achieving inclusion and fairness in policy interventions in cities, we present an open-source and data-driven framework to understand the spatial nature of accessibility to infrastructure among the different demographics. We find that accessibility to a wide range of infrastructure in any city (54 cities) converges to a Zipf's law, suggesting that inequalities also appear proportional to growth processes in these cities. Then, assessing spatial inequalities among the socioeconomically clustered urban profiles for 10 of those cities, we find urban communities are distinctly segregated along social and spatial lines. We find low accessibility scores for populations who have a larger share of minorities, earn less, and have a relatively lower number of individuals with a university degree. These findings suggest that the reproducible framework we propose may be instrumental in understanding processes leading to spatial inequalities and in supporting cities to devise targeted measures for addressing inequalities for certain underprivileged communities.