The proliferation of shared electric scooters (E-scooters) has brought convenience to urban transportation but has also introduced challenges such as disorderly parking and an imbalance between supply and demand. Given the current inconsistent quantity and spatial distribution of shared E-scooters, coupled with inadequate research on deployment stations selection, we propose a novel maximal covering location problem (MCLP) based on distance tolerance. The model aims to maximize the coverage of user demand while minimizing the sum of distances from users to deployment stations. A deep reinforcement learning (DRL) was devised to address this optimization model. An experiment was conducted focusing on areas with high concentrations of shared E-scooter trips in Chicago. The solutions of location selection were obtained by DRL, the Gurobi solver, and the genetic algorithm (GA). The experimental results demonstrated the effectiveness of the proposed model in optimizing the layout of shared E-scooter deployment stations. This study provides valuable insights into facility location selection for urban shared transportation tools, and showcases the efficiency of DRL in addressing facility location problems (FLPs).