In this paper, a solar site selection problem motivated by a real-world case study to determine sustainable locations for establishing solar sites in the east of Iran is addressed. For this purpose, a hybrid multi-criteria decision-making (MCDM) approach is proposed that adopts best-worst method (BWM) to weight criteria and sub-criteria extracted from literature and applies grey relational analysis (GRA) and VIKOR to rank potential locations. Moreover, an innovative Monte Carlo simulation-based (MCSB) approach is applied to analyze sensitivity of GRA and VIKOR. In this approach, two functional measures of robustness are introduced in order to compare performance of the methods. Based on the obtained results, some criteria, including construction cost (0.125), initial investment (0.166), ecosystem destruction (0.103), solar radiation intensity (0.085), and distance to catchment basins (0.084) have considerable importance because their weight is more than the average amount of global weights (0.0625). Furthermore, Birjand, Sarbisheh, and Khezri are the best locations for establishment of solar sites. Based on the proposed MCSB approach, VIKOR has higher robustness than GRA in the both functional measures. From the perspective of renewable energy development in Iran, the proposed approach can be recommended to be applied in other provinces of Iran for finding the best locations for solar sites.