With the rapid development of demand-side management, battery energy storage is considered to be an important way to promote the flexibility of the user-side system. In this paper, a Stackelberg game (SG) based robust optimization for user-side energy storage configuration and basic electricity price decisions is proposed. Firstly, this paper put forward a two-stage energy management framework considering the interactive relationship between the supplier-side system and the user-side system. Secondly, based on the two-part electricity price mechanism, a bi-level optimal sizing of user-side energy storage is established in which robust dispatching is considered to deal with the uncertainty of renewable energy. Thus, a three-layer optimization model of “pricing on the power supply side–basic scenario configuration on the user side–worst-case scenario scheduling on the user side” is formulated. Through relaxing the state variables of energy storage in the configuration and scheduling models and combining Karush-Kuhn-Tucher conditions, the user-side model is transformed into a single-layer problem. A distributed algorithm based on the method of bisection is used to solve the two-stage SG problem. The simulation results demonstrate the basic electricity price and energy storage configuration suggestions and prove the superiority of the proposed method.