This research proposes an Internet of Things (IoT)-enabled adaptive robotic navigation framework tailored for smart campuses and urban mobility systems. It aims to overcome critical limitations in existing systems that rely on static data, lack real-time adaptability, and perform poorly in dynamic or adverse environments. The proposed system uniquely integrates heterogeneous real-time data sources including traffic, obstacle, and weather captured from IoT sensors into a unified decision-making architecture. It combines a graph neural network for dynamic environmental modeling, a convolutional neural network for obstacle mapping, and a multilayer perceptron for weather-aware path assessment. A proximal policy optimization-based reinforcement learning (RL) controller then computes continuous control actions. A novel multi-objective reward function adaptively adjusts priorities between travel time, energy efficiency, collision risk, and terrain stability based on the current IoT context, enabling fine-grained, scenario-aware optimization. The system is deployed on resource-constrained edge hardware (Jetson Nano), proving its feasibility for real-time embedded applications. Simulations across diverse scenarios including urban traffic congestion, dynamic obstacle handling, and adverse weather demonstrate 95% navigation accuracy, 98% obstacle detection precision, and near-optimal route selection. The framework sustains real-time operation with 10 Hz decision throughput and sub-300 ms latency, outperforming traditional static and rule-based systems while sustaining over 92% performance consistency under adverse weather. This work introduces a first-of-its-kind modular framework that fuses IoT sensory data, adaptive RL control, and edge deployment for robust, efficient navigation. It establishes a scalable baseline for real-world autonomous mobility in smart city ecosystems.