Race and class disparities in COVID-19 cases are well documented, but pathways of possible transmission by neighborhood inequality are not. This study uses administrative data on COVID-19 cases for roughly 2000 census tracts in Wisconsin, Seattle/King County, and San Francisco to analyze how neighborhood socioeconomic (dis)advantage predicts cumulative caseloads through February 2021. Unlike past research, we measure a neighborhood's disadvantage level using both its residents' demographics and the demographics of neighborhoods its residents visit and are visited by, leveraging daily mobility data from 45 million mobile devices. In all three jurisdictions, we find sizable disparities in COVID-19 caseloads. Disadvantage in a neighborhood's mobility network has greater impact than its residents' socioeconomic characteristics. We also find disparities by neighborhood racial/ethnic composition, which can be explained, in part, by residential and mobility-based disadvantage. Neighborhood conditions measured before a pandemic offer substantial predictive power for subsequent incidence, with mobility-based disadvantage playing an important role.