As smart cities become increasingly dynamic and data-rich, real-time decision-making at the edge is essential to meet latency, privacy, and bandwidth requirements. Traditional cloud-based AI systems are limited by high communication overhead and a lack of context sensitivity. This paper proposes a novel Adaptive Edge AI framework that performs context-aware inference directly on resource-constrained edge devices. The system dynamically adapts AI model behaviour based on changing urban conditions such as traffic density, pedestrian flow, air quality, or environmental context through a lightweight, modular inference engine. Results show improvements in inference accuracy, latency, and resource efficiency compared to static edge AI deployments. This work offers a scalable approach to deploying intelligent, context-aware services across city infrastructure while maintaining local autonomy and robustness.