Location-Based Social Networks (LBSNs) have been widely used as a primary data source for studying the impact of mobility and social relationships on each other. Traditional approaches manually define features to characterize users' mobility homophily and social proximity, and show that mobility and social features can help friendship and location prediction tasks, respectively. However, these hand-crafted features not only require tedious human efforts, but also are difficult to generalize. Against this background, we propose LBSN2Vec++, a heterogeneous hypergraph embedding approach designed specifically for LBSN data for automatic feature learning. Specifically, LBSN data intrinsically forms a heterogeneous hypergraph including both user-user edges (friendships) and user-time-POI-semantic heterogeneous hyperedges (check-ins). Based on this hypergraph, we first propose a random-walk-with-stay scheme to jointly sample user check-ins and social relationships, and then learn node embeddings from the sampled (hyper)edges by not only preserving the n-wise node proximity captured by the hyperedges, but also considering embedding space transformation between node domains to fully grasp the complex structure of the LBSN heterogeneous hypergraph. Using real-world LBSN datasets, our evaluation shows that LBSN2Vec++ significantly outperforms state-of-the-art graph embedding techniques by up to 68% and the best-performing hand-crafted features by up to 70.14% on friendship and location prediction tasks.