Accurate localization of fovea is one of the primary steps in analyzing retinal diseases since it helps prevent irreversible vision loss. Although current deep learning-based methods achieve better performance than traditional methods, there still remain challenges such as utilizing anatomical landmarks insufficiently, sensitivity to diseased retinal images and various image conditions. In this paper, we propose a novel transformer-based architecture (Bilateral-Fuser) for multi-cue fusion. This architecture explicitly incorporates long-range connections and global features using retina and vessel distributions for robust fovea localization. We introduce a spatial attention mechanism in the dual-stream encoder for extracting and fusing self-learned anatomical information. This design focuses more on features distributed along blood vessels and significantly decreases computational costs by reducing token numbers. Our comprehensive experiments show that the proposed architecture achieves state-of-the-art performance on two public and one large-scale private datasets. We also present that the Bilateral-Fuser is more robust on both normal and diseased retina images and has better generalization capacity in cross-dataset experiments.