Healthcare facility site selection is one of the most complex multi-criteria decision-making problems owing to the involvement of numerous factors, including multiplestakeholders, conflicting objectives, and significant uncertainty across social,economic, environmental, and operational dimensions. Inappropriate site selection may lead to accessibility issues, congestion, environmental impacts, and high future relocation costs, particularly in newly developed urban areas. To address these challenges, this study proposes a novel neutrosophic decision-making framework that integrates the Neutrosophic Best–Worst Method (N-BWM) for criteria weighting with the Neutrosophic Ranking of Alternatives by Perimeter Similarity (N-RAPS) and the Neutrosophic Multiple Criteria Ranking by Alternative Trace (N-MCRAT) for alternative evaluation. To the best of the authors’ knowledge, this is the first application of N-RAPS and N-MCRAT within a neutrosophic environment. The proposed framework is applied to select the most sustainable site for a healthcare facility in Ras Al-Hakima as a real-world case study. The results indicate that A5 is the most consistent alternative, achieving the highest ranking across multiple scenarios and demonstrating strong robustness under varying decision priorities. A comparative analysis with established Multi-criteria decision-making (MCDM) techniques, including TOPSIS, VIKOR, MOORA, and fuzzy-based methods, confirms the stability and reliability of the proposed framework while highlighting its enhanced capacity to handle uncertainty. The findings suggest that the proposed methodology provides an effective and practical decision-support tool for sustainable healthcare planning and urban development.