New York City has been one of the hotspots of the COVID-19 pandemic and during the first two months of the outbreak considerable variability in case positivity was observed across the city's ZIP codes. In this study, we examined: a) the extent to which the variability in ZIP code level cases can be explained by aggregate markers of socioeconomic status and daily change in mobility; and b) the extent to which daily change in mobility independently predicts case positivity. Our analysis indicates that the markers considered together explained 56% of the variability in case positivity through April 1 and their explanatory power decreased to 18% by April 30. Our analysis also indicates that changes in mobility during this time period are not likely to be acting as a mediator of the relationship between ZIP-level SES and case positivity. During the middle of April, increases in mobility were independently associated with decreased case positivity. Together, these findings present evidence that heterogeneity in COVID-19 case positivity in New York City is largely driven by neighborhood socioeconomic status.