As a flexible, inexpensive, and extensive Internet access network, we have studied WIM-NET (Wireless Internet-access Mesh NETwork) composed of multiple access points (APs) as wireless mesh routers. WIMNET utilizes two types of APs to achieve the scalability with sufficient bandwidth while reducing costs. One is the expensive, programmable smart AP (SAP) that can use plural channels for wireless communications and has various functions for the Internet access. Another is the inexpensive, nonprogrammable conventional AP (CAP) that can use only one channel. To enhance the performance, the proper SAP allocation is critical, because the number of SAPs is much smaller than that of CAPs. In this paper, we present the definition of the SAP allocation problem, and its algorithm of extracting the optimum solution in terms of the newly defined cost function after finding the communication route configuration by applying our previous algorithms. We verify the effectiveness through simulations in three network topologies using the WIMNET simulator.