This study addresses sustainable urban heritage management needs through an AI-optimized methodology for Government-Museum networks. Integrating dramaturgical storytelling with computational intelligence, we develop a framework combining Freytag's Pyramid narrative framework with a hybrid Particle Swarm Optimization (PSO)-Machine Learning (ML) model. This sustainability-driven design aligns spatial routing with low-carbon objectives and thematic continuity, enhancing tourist itineraries while reducing environmental impact. Our model integrates GIS analysis of museum connectivity, accessibility criteria, and emissions indicators. Validated via Orange ML, the PSO-ML model achieves route optimization by minimizing distance, time, and CO₂ emissions. Results demonstrate significantly reduced travel distances/emissions and improved narrative coherence. The paradigm advances geographical justice, operational efficiency, and AI-mobility systems in promoting urban sustainability.