The devastating historical impact and increasing threat of natural disasters due to climate change have demonstrated the need for improved emergency relief efforts in disaster-prone areas like the Caribbean. In support of current problems faced by the Caribbean Disaster Emergency Management Agency (CDEMA), we explore an optimal prepositioning of hurricane emergency relief items under an uncertain hurricane trajectory. This work develops a data-driven prepositioning model in two ways, both prioritizing demand for relief over cost minimization to better align with the needs of Caribbean communities. First, we determine the optimal locations to place storage warehouses in the Caribbean by solving a demand-weighted minisum location problem. Prior to the hurricane landing, we then use bi-objective stochastic minimization to determine the optimal prepositioning inventory for each warehouse based on municipality relief distribution under different hurricane scenarios. The dual goals of this optimization problem are to minimize the expected largest region-level unmet demand and to minimize the expected largest region-level proportion of unmet demand. We find that the prepositioning approach improves allocated prepositioned supply from Hurricane Dorian, a 2019 hurricane that devastated by the Bahamas, by an aggregate 55% relative to the true strategy, providing needed resources faster and reducing potential loss of life in the immediate days after. This work ultimately lays mathematical and computational foundations to drive hurricane disaster preparedness insights that better serve the needs of people in the Caribbean.