Promoting the accessibility of basic public service facilities is key to safeguarding and improving people’s lives. Effective public service provision is especially important for the sustainable development of less developed regions. Lincang in Yunnan Province is a typical underdeveloped region in China. In parallel, multisource remote sensing data with higher spatial resolution provide more precise results for small-scale regional accessibility assessment. Thus, we use an assessment method to measure and evaluate the accessibility of three types of infrastructure in Lincang based on multisource geospatial data. We further analyze the matching between public service facility accessibility and the socioeconomic attributes of inhabitant clusters and different poverty groups. The results show that the accessibility of educational facilities is currently better than that of health facilities in Lincang and that of sanitation facilities is relatively poor. Public service facility accessibility varies significantly among different types of inhabitant clusters, with better accessibility in inhabitant clusters with high levels of population density, aging, and income. Accessibility to healthcare, education, and sanitation is negatively correlated to varying degrees of poverty levels of poor groups, and the mean values of accessibility to various types of public facilities vary significantly across poor groups. Our findings can help inform policy formulation and provide theoretical support for planning and optimizing the layout of public facilities.