The point-of-interest (POI) recommendation predicts users' destinations, which might be of interest to users and has attracted considerable attention as one of the major applications in location-based social networks (LBSNs). Recent work on graph-based neural networks (GNN) or matrix factorization-based (MF) approaches has resulted in better representations of users and POIs to forecast users' latent preferences. However, they still suffer from the implicit feedback and cold-start problems of check-in data, as they cannot capture both local and global graph-based relations among users (or POIs) simultaneously, and the cold-start neighbors are not handled properly during graph convolution in GNN. In this paper, we propose an enhanced encoder-decoder network (EEDN) to exploit rich latent features between users, POIs, and interactions between users and POIs for POI recommendation. The encoder of EEDN utilizes a hybrid hypergraph convolution to enhance the aggregation ability of each graph convolution step and learns to derive more robust cold-start-aware user representations. In contrast, the decoder mines local and global interactions by both graph- and sequential-based patterns for modeling implicit feedback, especially to alleviate exposure bias. Extensive experiments in three public real-world datasets demonstrate that EEDN outperforms state-of-the-art methods. Our source codes and data are released at https://github.com/WangXFng/EEDN