This paper introduces a graph-based dynamic model for electric vehicle (EV) mobility in urban areas. The model tracks EV state-of-charge (SoC) changes over time and space, along with power inputs from public charging stations (PCS). It considers driver behavior when deciding when and where to charge, accounting for factors like current SoC, distance to PCS, and charging cost. The model helps identify optimal PCS locations to enhance convenience for EV users and profitability for PCS owners. Additionally, an averaged version of the model is presented to reduce computational overhead while aiding in optimal PCS placement. Simulation results affirm the effectiveness of our model and optimization approach in identifying ideal charging station locations and enhancing EV charging infrastructure accessibility.