Urban transportation planning faces increasing complexity as cities seek to optimize mobility systems without extensive historical data. This paper presents CI-SGNN (City-Invariant Spatial Graph Neural Network), a novel framework for cross-city bike-sharing demand prediction that leverages Point of Interest (POI) distributions and spatial attention mechanisms. Our approach addresses the critical challenge of predicting categorical mobility demand in new urban environments by learning transferable relationships between urban amenities and travel patterns from source cities. The framework integrates OpenStreetMap POI features with GNNs, enabling zero-shot transfer learning across diverse metropolitan areas. We formulate demand prediction as a multi-class classification problem, categorizing origin-destination pairs into five demand levels. Experimental validation using real CitiBike data from Manhattan and Washington DC demonstrates superior performance, achieving 72.4% accuracy, which overperforms state-of-the-art base-lines. The attention-based spatial aggregation mechanism effectively captures inter-zone dependencies. Our results demonstrate successful zero-shot adaptation capabilities, enabling practical deployment for bike-sharing infrastructure planning in cities lacking historical mobility data using only publicly available urban features.