In the modern tourism industry, next point-of-interest (POI) recommendation is an important mobile service as it effectively aids hesitating travelers to decide the next POI to visit. Currently, most next POI recommender systems are built upon a cloud-based paradigm, where the recommendation models are trained and deployed on the powerful cloud servers. When a recommendation request is made by a user via mobile devices, the current contextual information will be uploaded to the cloud servers to help the well-trained models generate personalized recommendation results. However, in reality, this paradigm heavily relies on high-quality network connectivity, and is subject to high energy footprint in the operation and increasing privacy concerns among the public. To bypass these defects, we propose a novel Light Location Recommender System (LLRec) to perform next POI recommendation locally on resource-constrained mobile devices. To make LLRec fully compatible with the limited computing resources and memory space, we leverage FastGRNN, a lightweight but effective gated Recurrent Neural Network (RNN) as its main building block, and significantly compress the model size by adopting the tensor-train composition in the embedding layer. As a compact model, LLRec maintains its robustness via an innovative teacher-student training framework, where a powerful teacher model is trained on the cloud to learn essential knowledge from available contextual data, and the simplified student model LLRec is trained under the guidance of the teacher model. The final LLRec is downloaded and deployed on users' mobile devices to generate accurate recommendations solely utilizing users' local data. As a result, LLRec significantly reduces the dependency on cloud servers, thus allowing for next POI recommendation in a stable, cost-effective and secure way. Extensive experiments on two large-scale recommendation datasets further demonstrate the superiority of our proposed solution.