In this study we measure and map the system-wide spatial accessibility to good quality nursing home care for all counties in the contiguous United States, and use an 'imputed post-lasso' machine learning technique to systematically examine this accessibility measure's associations with a broad range of county-level socio-demographic variables. Both steps were carried out using publicly available datasets. Analyses found clear evidence of spatial patterning in accessibility, particularly by population density, state and the populations of specific racial minorities. This has implications for outcomes that extend beyond the care homes and we highlight a number of policy measures that may help to address these shortcomings. The 'out-of-sample' predictive performance of the machine learning approach highlights the method's usefulness in identifying systematic differences in accessibility to services.