This paper addresses multi-agent deployment in non-convex and uneven environments. To overcome the limitations of traditional approaches, we introduce Navigable Exemplar-Based Dispatch Coverage (NavEX), a novel dispatch coverage framework that combines exemplar-clustering with obstacle-aware and traversability-aware shortest distances, offering a deployment framework based on submodular optimization. NavEX provides a unified approach to solve two critical coverage tasks: (a) fair-access deployment, aiming to provide equitable service by minimizing agent-target distances, and (b) hotspot deployment, prioritizing high-density target regions. A key feature of NavEX is the use of exemplar-clustering for the coverage utility measure, which provides the flexibility to employ non-Euclidean distance metrics that do not necessarily conform to the triangle inequality. This allows NavEX to incorporate visibility graphs for shortest-path computation in environments with planar obstacles, and traversability-aware RRT* for complex, rugged terrains. By leveraging submodular optimization, the NavEX framework enables efficient, near-optimal solutions with provable performance guarantees for multi-agent deployment in realistic and complex settings, as demonstrated by our simulations.