Understanding how urban residents travel between neighborhoods and destinations is critical for transportation planning, mobility management, and public health. By mining historical origin-to-destination flow patterns with spatial, temporal, and functional relations among urban places, we estimate probabilities of visits from neighborhoods to specific destinations. These probabilities capture neighborhood-level contributions to citywide vehicular and foot traffic, supporting demand estimation, accessibility assessment, and multimodal planning. Particularly, we introduce VisitHGNN, a heterogeneous, relation-specific graph neural network designed to predict visit probabilities at individual Points of interest (POIs). POIs are characterized using numerical, JSON-derived, and textual attributes, augmented with fixed summaries of POI--POI spatial proximity, temporal co-activity, and brand affinity, while census block groups (CBGs) are described with 72 socio-demographic variables. CBGs are connected via spatial adjacency, and POIs and CBGs are linked through distance-annotated cross-type edges. Inference is constrained to a distance-based candidate set of plausible origin CBGs, and training minimizes a masked Kullback-Leibler (KL) divergence to yield probability distribution across the candidate set. Using weekly mobility data from Fulton County, Georgia, USA, VisitHGNN achieves strong predictive performance with mean KL divergence of 0.287, MAE of 0.008, Top-1 accuracy of 0.853, and R-square of 0.892, substantially outperforming pairwise MLP and distance-only baselines, and aligning closely with empirical visitation patterns (NDCG@50 = 0.966); Recall@5 = 0.611). The resulting distributions closely mirror observed travel behavior with high fidelity, highlighting the model's potential for decision support in urban planning, transportation policy, mobility system design, and public health.