Flight delays remain a major challenge for airline operations, resulting in increased costs, reduced passenger satisfaction, and scheduling complexities. To address these issues, we introduce a Spatio-Temporal Graph Attention Network (ST-GAT) that captures both temporal dynamics and spatial interdependencies among airports. Unlike conventional methods such as Random Forest, XGBoost, LSTM, or TCN, our ST-GAT constructs a graph where airports are nodes and flight routes are edges, enabling the model to learn how delays propagate through the network. By integrating attention mechanisms, the framework highlights critical airport connections and refines predictions with contextual awareness. Empirical evaluations on real-world flight datasets show that ST-GAT outperforms traditional deep learning approaches and benefits from careful hyperparameter tuning, achieving a mean absolute error (MAE) of 4.68. The model demonstrates a clear understanding of delay propagation, offering valuable insights for stakeholders. Additionally, it achieves an accuracy of 89.2%, further validating its predictive capabilities. These results suggest that graph-based deep learning can enhance flight delay prediction, leading to more resilient scheduling and improved passenger experiences. Our ST-GAT approach lays the groundwork for future research integrating additional data sources (e.g., weather, operational constraints) to further refine predictive accuracy in complex aviation environments.