Rapid growth in parcel delivery and increasing demand for time-sensitive freight, such as fresh food and pharmaceuticals, have intensified the need for fast and congestion-resilient urban logistics systems. However, ground-based logistics infrastructure in dense metropolitan areas is already highly saturated, and further facility expansion is often spatially and operationally constrained. This study proposes a multi-period facility location model for an integrated air–ground–underground urban logistics system that connects Urban Air Mobility, ground vehicles, and subway-based freight transportation with existing logistics infrastructure. Unlike conventional hub location or multi-echelon facility location problems, the proposed model determines whether candidate locations can serve as integrated logistics hubs capable of supporting multimodal transshipment among aerial, ground, and underground transportation modes. Candidate sites include existing large-scale ground terminals, micro-fulfillment centers, subway stations suitable for underground logistics facilities, and vacant sites where new facilities can be constructed. The model simultaneously considers facility construction and operation decisions, inter-hub freight flows, last-mile delivery allocation, unmet demand penalties, transshipment costs, and annual budget constraints over multiple planning periods. The proposed framework also reflects the shared-use nature of UAM infrastructure by considering the interaction between passenger and freight demand when estimating available cargo capacity. To examine the applicability of the model, a case study is conducted for the Seoul metropolitan area, where ground logistics facilities are highly saturated and subway infrastructure is widely distributed. The results demonstrate that the proposed model can support phased investment decisions for multimodal logistics hubs and provide strategic insights for improving the responsiveness of time-sensitive urban freight delivery.