Hierarchical structures and organizational models highly affect the sustainable operation of the spatial network of tourism destinations. This paper adopted the modified tourism gravity model and social network analysis method to reveal the spatial characteristics of the tourism network on the Tibetan Plateau based on tourism flow data in 2019. The results are as follows: (1) the spatial organization of tourism flows was unbalanced, showing the characteristics of “high in the east and low in the west”; (2) The county tourism flow formed a multidimensional system of spatial hierarchy with Chengguan District of Lhasa, Golmud City, and Pengzhou City as the top nodes, the spatial polarization characteristics, and zonal distribution differences were evident; (3) The inter-county tourism linkage conformed to the law of distance decay, and the multiple network structure hierarchy features highlighted the complex linkage pattern; (4) The tourism network had a more distinctive dominant flow and was influenced by county-level administrative divisions; (5) The tourism linkage network formed eight subgroups with significant geographical characteristics. This study provides recommendations for optimizing the spatial structure of the Tibetan Plateau county tourism network for the government.