Biological systems possess remarkable sound source localization (SSL) capabilities that are critical for survival in complex environments. This ability arises from the collaboration between the auditory periphery, which encodes sound as precisely timed spikes, and the auditory cortex, which performs spike-based computations. Inspired by these biological mechanisms, we propose a novel neuromorphic SSL framework that integrates spike-based neural encoding and computation. The framework employs Resonate-and-Fire (RF) neurons with a phase-locking coding (RF-PLC) method to achieve energy-efficient audio processing. The RF-PLC method leverages the resonance properties of RF neurons to efficiently convert audio signals to time-frequency representation and encode interaural time difference (ITD) cues into discriminative spike patterns. In addition, biological adaptations like frequency band selectivity and short-term memory effectively filter out many environmental noises, enhancing SSL capabilities in real-world settings. Inspired by these adaptations, we propose a spike-driven multi-auditory attention (MAA) module that significantly improves both the accuracy and robustness of the proposed SSL framework. Extensive experimentation demonstrates that our SSL framework achieves state-of-the-art accuracy in SSL tasks. Furthermore, it shows exceptional noise robustness and maintains high accuracy even at very low signal-to-noise ratios. By mimicking biological hearing, this neuromorphic approach contributes to the development of high-performance and explainable artificial intelligence systems capable of superior performance in real-world environments.