In a large, international study of urban residents, researchers found that only access to green space and recreational areas made a difference in reducing neighborhood socioeconomic health inequalities, while financial services, transport, and cultural facilities had no effect.
Mitchell, Richard J., Elizabeth A. Richardson, Niamh K. Shortt, and Jamie R. Pearce. (2015). Neighborhood Environments and Socioeconomic Inequalities in Mental Well-Being. American Journal of Preventive Medicine.