The rapid growth of Internet of Things (IoT) devices and the increasing demand for low-latency services in smart city environments have made efficient edge server placement (ESP) a critical challenge in mobile edge computing (MEC) systems. Effective placement of edge servers is essential for reducing network delays and achieving balanced workload distribution across servers, both of which directly affect the user experience. This paper addresses the ESP problem by formulating it as a multi-objective optimization problem that simultaneously minimizes the average distance between edge servers and base stations while reducing workload imbalance among the servers. To tackle this challenge, we propose an Iterative Weighted Randomized Algorithm (IWRA). The algorithm generates multiple potential placement solutions by employing a weighted roulette wheel selection, where base station weights are determined by their workloads. For each solution, edge servers are iteratively assigned to base stations, and clusters are formed by associating each base station with the nearest server. The solutions are evaluated based on normalized access distance and workload standard deviation, and the solution with the best score is selected as the final placement configuration. We validated the proposed algorithm through extensive simulations using both synthetic datasets and a real-world dataset from Shanghai Telecom, covering diverse network scenarios. The results demonstrate that our approach outperforms conventional placement methods, such as Random and Top-K placement, achieving an average reduction of 33% in access distance and a 27% improvement in workload balancing. These findings underscore the superior effectiveness of our method in addressing the ESP problem.