Sharing sensitive data is vital in enabling many modern data analysis and machine learning tasks. However, current methods for data release are insufficiently accurate or granular to provide meaningful utility, and they carry a high risk of deanonymization or membership inference attacks. In this paper, we propose a differentially private synthetic data generation solution with a focus on the compelling domain of location data. We present two methods with high practical utility for generating synthetic location data from real locations, both of which protect the existence and true location of each individual in the original dataset. Our first, partitioning-based approach introduces a novel method for privately generating point data using kernel density estimation, in addition to employing private adaptations of classic statistical techniques, such as clustering, for private partitioning. Our second, network-based approach incorporates public geographic information, such as the road network of a city, to constrain the bounds of synthetic data points and hence improve the accuracy of the synthetic data. Both methods satisfy the requirements of differential privacy, while also enabling accurate generation of synthetic data that aims to preserve the distribution of the real locations. We conduct experiments using three large-scale location datasets to show that the proposed solutions generate synthetic location data with high utility and strong similarity to the real datasets. We highlight some practical applications for our work by applying our synthetic data to a range of location analytics queries, and we demonstrate that our synthetic data produces near-identical answers to the same queries compared to when real data is used. Our results show that the proposed approaches are practical solutions for sharing and analyzing sensitive location data privately.