Learning effective geospatial embeddings is crucial for a series of geospatial applications such as city analytics and earth monitoring. However, learning comprehensive region representations presents two significant challenges: first, the deficiency of effective intra-region feature representation; and second, the difficulty of learning from intricate inter-region dependencies. In this paper, we present GeoHG, an effective heterogeneous graph structure for learning comprehensive region embeddings for various downstream tasks. Specifically, we tailor satellite image representation learning through geo-entity segmentation and point-of-interest (POI) integration for expressive intra-regional features. Furthermore, GeoHG unifies informative spatial interdependencies and socio-environmental attributes into a powerful heterogeneous graph to encourage explicit modeling of higher-order inter-regional relationships. The intra-regional features and inter-regional correlations are seamlessly integrated by a model-agnostic graph learning framework for diverse downstream tasks. Extensive experiments demonstrate the effectiveness of GeoHG in geo-prediction tasks compared to existing methods, even under extreme data scarcity (with just 5% of training data). With interpretable region representations, GeoHG exhibits strong generalization capabilities across regions. We will release code and data upon paper notification.