This study develops a new method to quantify neighborhood activity levels at high spatial and temporal resolutions and test whether, and to what extent, behavioral responses to social distancing policies vary with socioeconomic and demographic characteristics. We define exposure density as a measure of both the localized volume of activity in a defined area and the proportion of activity occurring in non-residential and outdoor land uses. We utilize this approach to capture inflows/outflows of people as a result of the pandemic and changes in mobility behavior for those that remain. First, we develop a generalizable method for assessing neighborhood activity levels by land use type using smartphone geolocation data over a three-month period covering more than 12 million unique users within the Greater New York area. Second, we measure and analyze disparities in community social distancing by identifying patterns in neighborhood activity levels and characteristics before and after the stay-at-home order. Finally, we evaluate the effect of social distancing in neighborhoods on COVID-19 infection rates and outcomes associated with localized demographic, socioeconomic, and infrastructure characteristics in order to identify disparities in health outcomes related to exposure risk. Our findings provide insight into the timely evaluation of the effectiveness of social distancing for individual neighborhoods and support a more equitable allocation of resources to support vulnerable and at-risk communities. Our findings demonstrate distinct patterns of activity pre- and post-COVID across neighborhoods. The variation in exposure density has a direct and measurable impact on the risk of infection.