The growing penetration of renewable energy sources, with intermittent and uncertain nature, brings new challenges to the secure and efficient operation of power systems. Expanding transmission networks and utilizing energy storage (ES) have been introduced as effective solutions to address these challenges. This paper presents a minimax regret co-planning model for transmission and ES systems from the perspective of a central planner under a polyhedral uncertainty set of future peak load growth and uncertainties of wind farm expansion addressed through internal scenario analysis. This minimax regret robust approach will guarantee the robustness of the investment decisions and provide the central planner with a clear picture of the maximum regret among all possible scenarios. However, solving the proposed model is challenging due to the infinite number of scenarios and constraints associated with all realizations of uncertain parameters of polyhedral uncertainty sets. Therefore, a five-level solution strategy based on the nested column and constraint generation (C&CG) decomposition technique is represented to deal with the intractability and complexity of the problem caused by binary variables of transmission lines and ES blocks. The model is finally implemented on a modified IEEE 24-bus test system to verify its tractability, practicality, and effectiveness.