Tehran’s District 12, as one of the capital’s cultural and tourism hubs, hosts a collection of prominent cultural institutions and museums that serve as major attractions for domestic and international visitors. However, the absence of systematic planning for routing between these centers leads to wasted time and energy for tourists and diminishes the quality of their visitation experience. This study aims to optimize museum visitation routes in Tehran’s District 12, focusing on minimizing travel time and distance, by selecting 22 active and significant museums in the area as case studies. To achieve this, the mathematical model of the Open Traveling Salesman Problem (Open TSP) was applied within the framework of network analysis in a Geographic Information System (GIS) environment. Precise spatial data—including the geographic locations of museums and the local street network—were imported into ArcGIS software and processed using the Network Analyst tool. Travel cost matrices (based on time and distance) between all museum pairs were calculated, and optimal visitation routes were extracted and ranked using heuristic Open TSP algorithms according to the criteria of minimum time and shortest distance. Findings indicate that applying the Open TSP model within network analysis leads to the identification of significantly more efficient routes compared to conventional patterns or unplanned visits. Quantitative results show that, under normal (non-optimized) conditions, visiting all 22 museums covers a distance of 25.91 km with a travel time of 310 minutes, whereas the optimized proposed route requires only 9.896 km and 118 minutes of travel time. This improvement represents a 62% reduction in both distance and travel time. The study demonstrates the high efficiency of integrating combinatorial optimization models with GIS spatial analysis capabilities for urban tourism planning and can serve as a model for intelligent management of tourist visitation routes in other urban areas. The results enable informed decision-making and optimal planning for both group and individual visits, significantly enhancing the tourism experience by reducing time and physical costs.