Vision-based locomotion has shown great promise in enabling legged robots to perceive and adapt to complex environments. However, visual information is inherently fragile, being vulnerable to occlusions, reflections, and lighting changes, which often cause instability in locomotion. Inspired by animal sensorimotor integration, we propose KiVi, a Kinesthetic-Visuospatial integration framework, where kinesthetics encodes proprioceptive sensing of body motion and visuospatial reasoning captures visual perception of surrounding terrain. Specifically, KiVi separates these pathways, leveraging proprioception as a stable backbone while selectively incorporating vision for terrain awareness and obstacle avoidance. This modality-balanced, yet integrative design, combined with memory-enhanced attention, allows the robot to robustly interpret visual cues while maintaining fallback stability through proprioception. Extensive experiments show that our method enables quadruped robots to stably traverse diverse terrains and operate reliably in unstructured outdoor environments, remaining robust to out-of-distribution (OOD) visual noise and occlusion unseen during training, thereby highlighting its effectiveness and applicability to real-world legged locomotion.