This paper formulates Advanced Air Mobility (AAM) emergency logistics infrastructure planning as an energy-constrained facility-location problem applied to the 21-county Northeastern North Carolina (NENC) region. A reduced-order physics-based energy model evaluates depot-to-county mission feasibility under battery capacity (40, 60, 80 kWh), payload (35 kg/77lbs and 113 kg/250lbs), mission type (one-way vs. round-trip), and wind conditions. The resulting binary coverage matrix drives three integer programming models: set covering, maximum coverage location (MCLP), and p-median assignment. An equity extension incorporates CDC Social Vulnerability Index weights. A dual-depot scenario pairing Elizabeth City with Edenton (Chowan County), drawn from a prior routing simulation in this research series, is also evaluated. Key findings: Elizabeth City as a single depot covers 66.7% of NENC counties under 40 kWh round-trip constraints, while an optimally placed single depot achieves 95.2%, missing only Vance County; two strategically placed vertiports achieve complete 100% coverage at 40 kWh round-trip, and a single depot suffices at 60 kWh; the Elizabeth City–Edenton dual-depot configuration achieves complete coverage under both one-way and round-trip missions at 60 kWh; under the tested NENC geography, uniform-wind assumption, and capped wind-energy model, battery capacity, not wind, is the dominant infrastructure lever. Equity analysis confirms that the optimized two-depot network covers all eight of the highest social-vulnerability counties, including Tyrrell (SVI = 0.96), Hyde (0.95), and Northampton (0.93), eliminating the equity gap present under the single-depot baseline, where these communities remain unserved. Results provide a quantitative foundation for phased AAM emergency logistics infrastructure planning in NENC.