The deployment of vaccines across the US provides significant defense against serious illness and death from COVID-19. Over 70% of vaccine-eligible Americans are at least partially vaccinated, but there are pockets of the population that are under-vaccinated, such as in rural areas and some demographic groups (e.g. age, race, ethnicity). These pockets are extremely susceptible to the Delta variant, exacerbating the healthcare crisis and increasing the risk of new variants. In this paper, we describe a data-driven model that provides real-time support to Virginia public health officials by recommending mobile vaccination site placement in order to target under-vaccinated populations. Our strategy uses fine-grained mobility data, along with US Census and vaccination uptake data, to identify locations that are most likely to be visited by unvaccinated individuals. We further extend our model to choose locations that maximize vaccine uptake among hesitant groups. We show that the top recommended sites vary substantially across some demographics, demonstrating the value of developing customized recommendation models that integrate fine-grained, heterogeneous data sources. We also validate our recommendations by analyzing the success rates of deployed vaccine sites, and show that sites placed closer to our recommended areas administered higher numbers of doses. Our model is the first of its kind to consider evolving mobility patterns in real-time for suggesting placement strategies customized for different targeted demographic groups.