Reliable assessment of safe landing sites in unstructured environments is essential for deploying Unmanned Aerial Vehicles (UAVs) in real-world applications such as delivery, inspection, and surveillance. Existing learning-based approaches often degrade under covariate shift and offer limited transparency, making their decisions difficult to interpret and validate on resource-constrained platforms. We present NeuroSymLand, a neuro-symbolic framework for marker-free UAV landing site safety assessment that explicitly separates perception-driven world modeling from logic-based safety reasoning. A lightweight segmentation model incrementally constructs a probabilistic semantic scene graph encoding objects, attributes, and spatial relations. Symbolic safety rules, synthesized offline via large language models with human-in-the-loop refinement, are executed directly over this world model at runtime to perform white-box reasoning, producing ranked landing candidates with human-readable explanations of the underlying safety constraints. Across 72 simulated and hardware-in-the-loop landing scenarios, NeuroSymLand achieves 61 successful assessments, outperforming four competitive baselines, which achieve between 37 and 57 successes. Qualitative analysis highlights its superior interpretability and transparent reasoning, while deployment incurs negligible edge overhead. Our results suggest that combining explicit world modeling with symbolic reasoning can support accurate, interpretable, and edge-deployable safety assessment in mobile systems, as demonstrated through UAV landing site assessment.