To improve the operational efficiency of electric vehicle (EV) charging infrastructure, this paper proposes a multi-stage hybrid planning method for charging stations (CSs) based on graph auto-encoder (GAE). First, the network topology and dynamic interaction process of the coupled “Vehicle-Station-Network” system are characterized as a graph-structured model. Second, in the first stage, a GAE-based deep neural network is used to learn the graph-structured model and identify and classify different charging station (CS) types for the network nodes of the coupled system topology. The candidate CS set is screened out, including fast-charging stations (FCSs), fast-medium-charging stations, medium-charging stations, and slow-charging stations. Then, in the second stage, the candidate CS set is re-optimized using a traditional swarm intelligence algorithm, considering the interests of multiple parties in CS construction. The optimal CS locations and charging pile configurations are determined. Finally, case studies are conducted within a practical traffic zone in Hong Kong, China. The existing CS planning methods rely on simulation topology, which makes it difficult to realize efficient collaboration of charging networks. However, the proposed scheme is based on the realistic geographical space and large-scale traffic topology. The scheme determines the station and pile configuration through multi-stage planning. With the help of an artificial intelligence (AI) algorithm, the user behavior characteristics are captured adaptively, and the distribution rule of established CSs is extracted to provide support for the planning of new CSs. The research results will help the power and transportation departments to reasonably plan charging facilities and promote the coordinated development of EV industry, energy, and transportation systems.