Battery swapping for electric vehicle refueling is reviving and thriving. Despite a captivating sustainable future where swapping batteries will be as convenient as refueling gas today, a tension is mounting in practice (beyond the traditional “range anxiety” issue): On one hand, it is desirable to maximize battery proximity and availability to customers. On the other hand, capacitated urban power grids may curb decentralized charging at a slow speed. To reconcile this tension, some cities are embracing an emerging infrastructure network: Decentralized swapping stations replenish charged batteries from centralized charging stations. It remains unclear how to design such a network or whether pooling charging demands will save costs or batteries. In this paper, we model this new urban infrastructure network. This task is complicated by non-Poisson swaps and by the intertwined stochastic operations of swapping, charging, stocking, and circulating batteries among swapping and charging stations. We tackle these complexities by deriving analytical models, which enrich the classical batched repairable-inventory theory. We next propose a joint location and repairable-inventory model for citywide deployment of hub charging stations, with a nonconvex nonconcave objective function. We solve this problem exactly by exploiting submodularity and combining constraint-generation and parameter-search techniques. Even for solving convexified problems, our algorithm brings a speedup of at least three orders of magnitude relative to the Gurobi solver. The major insight is twofold: The benefit of pooling charging demands alone is not enough to justify the adoption of the “swap-locally, charge-centrally” network; instead, the main justification is that faster charging accessible at centralized charging stations significantly reduces the system-wide battery stock level. In a broader sense, this work deepens our understanding of how mobility and energy are coupled toward enabling smart cities.