This research explores the development of privacy-aware graph neural networks (GNNs) designed for smart city environments. It aims to address the challenges of preserving privacy while leveraging GNNs to analyze and process the complex, interconnected graph data characteristic of smart cities. By integrating privacy-preserving techniques within GNN frameworks, this study contributes to ongoing efforts to enhance graph privacy in smart city applications. Furthermore, it lays a foundation for future research into advancing from privacy-focused methods to the broader development of trustworthy GNNs.