Reliable robotic navigation necessitates the seamless integration of accurate global localization and dense, metric-consistent obstacle perception. A common strategy to achieve these capabilities involves integrating diverse sensing modalities: cameras offer rich visual features for localization, while active sensors like LiDAR provide direct metric measurements. However, such multi-sensor configurations necessitate complex spatial-temporal calibration and increase deployment overhead. Although vision-only approaches offer a low-cost and scalable alternative, existing monocular visual systems typically struggle to simultaneously achieve efficient, globally consistent localization and dense, metric-consistent geometric perception. To bridge this gap, we propose \textbf{VGP-Nav}, a unified framework for \textit{Metric-Aware Visual Geometric Perception} that relies solely on monocular RGB input to jointly support metric localization and obstacle perception. Our key insight is to anchor localization-grounded visual geometry to physically meaningful scale constraints derived from ground-plane geometry, thereby providing a reliable metric reference for monocular perception. VGP-Nav resolves monocular scale ambiguity online and produces localization-grounded, metric obstacle representations that are directly applicable to downstream planning. Extensive experiments demonstrate strong generalization across diverse environments and successful deployment on real mobile robots, highlighting the practicality of our approach for scalable, low-cost, and safe autonomous navigation.