Hierarchical edge-cloud computing-aided Internet of Things (IoT) networks offer low-latency and cost-efficient services to a growing number of data-intensive IoT devices. However, optimizing service placement, which involves determining the most suitable locations within a network to deploy various services, is critical to balancing workloads dynamically and ensuring efficient resource utilization. In this paper, we jointly optimize service placement, edge/cloud cooperation, task offloading, and bandwidth allocation to enhance processing efficiency and response times. The main objective is to minimize both the overall end-to-end latency and the system cost, including service deployment and operational costs. The formulated problem belongs to the class of non-convex mixed-integer nonlinear programming, where finding a feasible solution is already challenging. Towards a stable system, we first transform the original problem into a more tractable form and then decompose it into sub-problems which are solved at different timescales. Combining tools from relaxation and the successive convex approximation method, we develop iterative algorithms to solve these problems efficiently. With an appropriate penalty parameter, the proposed algorithms guarantee convergence to at least a local optimum. We produce extensive numerical results to demonstrate the superior performance of the proposed algorithms over benchmark schemes as well as emphasize the significance of the joint service placement and resource allocation in enhancing system performance and efficiency.