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The past studies on router node placement for wireless mesh networks (WMNs) did not consider placement of Internet gateways. Therefore, mesh routers and mesh clients can only communicate locally. The problem in this paper is to maximize both network connectivity and client coverage for the router node placement in WMNs consisting of mesh routers, mesh clients, and Internet gateways, subject to three QoS constraints: delay, relay load, and Internet gateway capacity. By visualizing the placements in previous works, we discover two main drawbacks: overlapping and coverless. To solve them, this paper presents a novel particle swarm optimization approach. Performance of the proposed approach is verified by simulation.