This paper addresses the problem of robot navigation in mixed geometric/semantic 3D environments. Given a hierarchical representation of the environment, the objective is to navigate from a start position to a goal, while satisfying task-specific safety constraints and minimizing computational cost. We introduce Hierarchical Class-ordered A* (HCOA*), an algorithm that leverages the environment's hierarchy for efficient and safe path-planning in mixed geometric/semantic graphs. We use a total order over the semantic classes and prove theoretical performance guarantees for the algorithm. We propose three approaches for higher-layer node classification based on the semantics of the lowest layer: a Graph Neural Network method, a k-Nearest Neighbors method, and a Majority-Class method. We evaluate HCOA* in simulations on two 3D Scene Graphs, comparing it to the state-of-the-art and assessing the performance of each classification approach. Results show that HCOA* reduces the computational time of navigation by up to 50%, while maintaining near-optimal performance across a wide range of scenarios.