The spatial organization of tissues emerges from cell interactions across multiple scales, yet current spatial omics analysis tools often emphasize local neighborhoods and may not summarize broader tissue architecture. Here we introduce Cophenetic Spatial Topology Embedding (COSTE), a computational framework that embeds directed nearest-neighbor distance profiles into a hierarchical metric space without requiring the user to define a spatial radius or neighborhood cutoff. COSTE can be applied to cell-level and single-transcript inputs without requiring cell segmentation. It constructs directed distance profiles between cell populations and uses hierarchical clustering to quantify tissue topology. This yields a Spatial Separation Score (SSS), a sample-normalized score from 0 to 1 that summarizes relative spatial separation within an analyzed tissue. We apply COSTE to spatial transcriptomics datasets of pulmonary fibrosis and triple-negative breast cancer (TNBC), where it delineates tissue structures, nominates spatially defined cell states, and highlights disease-or treatment-associated architectural patterns that are not readily captured by local neighborhood-based analyses. Our approach provides an interpretable framework for exploring tissue architecture and cell-cell spatial relationships in spatial omics data.