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With the development and utilization of more and more city Internet of Things (IoT) applications with high resource requirements, how to reduce the consumption of energy, processor resources and bandwidth resources in resource-constrained edge clouds while ensuring the execution delay of these applications is an urgent problem to be solved. Therefore, an optimal energy-bandwidth tradeoff deployment approach for city IoT application is proposed for resource-constrained edge clouds. In this approach, the city IoT applications are first divided into multiple collaborative tasks and offload to edge clouds. Secondly, a joint optimization model including energy consumption, resource wastage, resource load imbalance and bandwidth resource consumption is established for the task offloading scheme. Thirdly, the city IoT application deployment problem is optimized under the constraints of resource and execution delay. Finally, a comprehensive simulation test is conducted to analyze the deployment approaches from the aspects of performance and effectiveness. The experimental results show that our deployment approach is superior to other related approaches.