Point-of-Interest (POI) recommendation plays a pivotal role in location-based services by guiding users to discover new and relevant places. While graph-based methods have shown promising results, effectively modeling the diversity and dynamics of user preferences remains a key challenge. Addressing this requires richer representations of both POIs and user interests, as well as more adaptive learning strategies. In this work, we propose TMHKG, a Task-aware Meta-learning framework with a Heterogeneous Knowledge Graph for POI recommendation. To enhance representation learning, TMHKG constructs a dual-view POI knowledge graph that integrates geographical proximity and user-aware category transitions, and models users' evolving interests from sequential visit histories. On top of enriched features, TMHKG adopts a task-aware meta-learning paradigm, treating each user's recommendation task as a separate meta-task. A generalizable recommendation policy is first learned from diverse training tasks and then quickly adapted to each user's unique behavior, enabling highly personalized predictions. Extensive experiments on two real-world datasets demonstrate that TMHKG consistently outperforms state-of-the-art baselines, highlighting its effectiveness in capturing complex user-POI interactions.