Wireless Mesh Networks (WMNs) are an important networking infrastructure for providing cost-efficient broadband wireless connectivity to a group of users. WMNs are increasingly being used in urban areas, metropolitan and municipal area networks for deployment of medical, transport, surveillance systems, etc. The good performance and operability of WMNs largely depends on placement of mesh routers nodes in the geographical area to achieve network connectivity and stability. Therefore, optimal placement of router nodes in WMNs is a main issue in deployment of WMNs. In this work we propose and evaluate local search methods for placement of mesh routers in WMNs with a two fold objective: maximizing the size of the giant component in the network and user coverage. Given a grid area where to distribute a given number of mesh router nodes, which can have different radio coverage, and a number of fixed clients a priori distributed in the given area, local search methods explore different local movements and incrementally improve the quality of the router nodes placement in terms of network connectivity and user coverage. We have experimentally evaluated the considered local search methods through a benchmark of generated instances varying from small to large size. In the instances, different distributions of mesh clients (Uniform, Normal, Exponential and Weibull) are considered aiming to evaluate the quality of achieved solutions for different client distributions. Although local search methods can be stuck in local optima, the experimental evaluation showed their good performance; local search methods could thus be applied as a first choice for optimizing network connectivity and user coverage in WMNs.