Exam timetabling problems have been vastly investigated mainly focusing on universities or schools where exams are concentrated in a single campus or building. The urge for exploring exam locations and participant assignments concerned with allocation distances and development of effective methods to tackle these challenges has therefore not been present in this field of study. However, the location and allocation decisions are of utmost importance when organizing nation-wide exams. This paper investigates how to address a real-world problem concerning the location of geographically-distributed exams. The challenge is in determining the best locations and allocations at a low cost with acceptable distances to be traversed by the participants. As the minimization of cost may adversely affect the allocation distances (and the other way around), it is crucial to determine how to incorporate the two conflicting measures in the decision-making process. Combining location costs and the costs associated with allocation distances in a single objective function may not always be straightforward or possible due to the lack of appropriate weights. Consulting alternative modeling viewpoints may then prove useful. We research the most convenient modeling approaches through binary integer programming formulations of several problem variants and extensions of the original real-world problem. Extensive computational experiments have been conducted to observe the behavior of the models and direct the research methodology. Important insights are demonstrated with the help of solution visualizations.