Image geolocalization is important for applications in crisis response, digital forensics, and location-based intelligence. While recent advances in large language models (LLMs) offer new opportunities for visual reasoning, their ability to perform image geolocalization remains underexplored. In this study, we introduce a benchmark called IMAGEO-Bench that systematically evaluates accuracy, distance error, geospatial bias, and reasoning process. Through experiments on 10 state-of-the-art LLMs, we reveal clear performance disparities, with closed-source models generally showing stronger reasoning. Importantly, we uncover systematic geospatial disparities: LLMs perform better in high-resource regions (e.g., North America, Western Europe, and California) while exhibiting degraded performance in underrepresented areas. Regression diagnostics demonstrate that successful geolocalization is strongly associated with recognizing urban settings, outdoor environments, street-level imagery, and identifiable landmarks. Overall, IMAGEO-Bench provides a rigorous lens into the spatial reasoning capabilities of LLMs and offers implications for building geolocation-aware AI systems.