Globalization and decentralization of production generate the intensive growth of goods and transport flows, mostly performed by the maritime transport. Ports, as the main nodes in the global logistics networks, are becoming congested, space for their expansion limited, and traffic in their hinterland congested. As a solution to these and many other hinterland-transport-related problems stands out the development of dry port (DP) terminals. Selection of their location is one of the most important strategic decisions on which depends their competitiveness in the market and the functionality of the logistics network. Accordingly, the evaluation and selection of locations for the development of the DP in accordance with the requirements of various stakeholders is performed in this paper, as a prerequisite for the establishment of an ecological, economic, and socially sustainable logistics network in the observed area. To solve this problem, a new hybrid model of multi-criteria decision-making (MCDM) that combines Delphi, AHP (Analytical Hierarchy Process), and CODAS (Combinative Distance-based Assessment) methods in a grey environment is developed. The main contributions of this paper are the defined model, the problem-solving approach based on finding a compromise solution, simultaneous consideration of the environmental, economic, and social sustainability of the DP concept and its implementation in the regional international markets. The applicability of the approach and the defined MCDM model is demonstrated by solving a real-life case study of ranking the potential DP locations in the Western Balkans region. Based on the obtained results, it is concluded that in the current market conditions, it would be most realistic to open three DP terminals, in Zagreb, Ljubljana, and Belgrade.