The historical monuments of the National Preserve “Kyiv-Pechersk Lavra” play an important role in the context of preserving the UNESCO World Heritage. The scientific understanding of the buildings and structures safety management the priority of conducting repair and restoration works, the organization of their technical condition monitoring, and changes in the components of the geological environment in their locations is crucial. The purpose of this study is to identify potentially hazardous areas on the territory of the Lavra for the operation of structures by conducting a point-based integral assessment of the stability potential of the natural and technogenic system with the integration of geospatial methods and to rank the structures using the analytical hierarchy process. According to the modeling results by 17 stability factors and using ArcGIS, 37% (8.7 ha) of the Lavra territory is located in the zone of moderate hazard, 23% (5.4 ha) in the zone of potential hazard, where the manifestation and conditions of more than five dangerous engineering and geological processes intersect, and 40% (9.4 ha) in the zone of relative safety. In each zone, 10 representative structures were selected for ranking according to the stability of natural and technogenic operating conditions and their current technical condition, which is determined by nine criteria. The analysis using two methods identified the areas most at risk from seasonal fluctuations and possible military impacts and allowed us to scientifically substantiate the priority of repair and restoration work and the possibility of properly planning management measures for the selected structures, as well as to offer recommendations for improving the monitoring of the geological environment of the Lavra.