In recent years, the awareness of sustainable tourism has risen around the world. Many tourism industries combine sports to attract more customers to facilitate the development of the economy and the promotion of local culture. However, it is an important task to establish a comprehensive tourism evaluation framework for sustainable sports tourism. This study proposes a Multi-Criteria Decision-Making (MCDM) model to discuss the above issues, using the Bayesian Best Worst Method (Bayesian BWM) to integrate multiple experts’ judgments to generate the group optimal criteria weights. Next, the modified Visekriterijumska Optimizacija i Kompromisno Resenje (VIKOR) technique is combined with the concept of aspiration level to determine the performance of sports attractions and their priority ranks. In addition, this study adds a perspective of institutional sustainability to emphasize the importance of government support and local marketing. The effectiveness and robustness of the proposed model is demonstrated through potential sports tourism attractions in Taiwan. A sensitivity analysis and models comparison were also performed in this study. The results show that the proposed model is feasible for practical applications and that it effectively provides some management implications to support decision-makers in formulating improvement strategies.