As the threat of quantum computing to classical cryptography grows, the transition to post-quantum cryptographic (PQC) systems becomes essential—particularly for smart city infrastructures that rely heavily on secure, real-time sensor data. This paper investigates the performance of PQC algorithms currently in the final stages of standardization by the U.S. National Institute of Standards and Technology (NIST), focusing on their deployment in resource-constrained Internet of Things (IoT) devices. Leveraging real-world smart city sensor datasets, we develop a research prototype that simulates a realistic urban sensing scenario, using Raspberry Pi 3 and Pi Zero 2 W devices to cryptographically secure and transmit data to a central server. Experimental results demonstrate that the Kyber family is the most efficient for key encapsulation tasks, while Dilithium and Falcon offer strong performance for digital signatures. In contrast, PQC algorithms such as McEliece, HQC, and Rainbow exhibit substantial computational overhead—especially at higher security levels—limiting their suitability for time-sensitive or low-power environments. Our findings highlight the practical implications of PQC adoption in smart cities and provide evidence-based guidance for selecting efficient quantum-safe algorithms for real-world urban sensor networks.