In 60 GHz wireless networks, autonomous coordinator selection is required to find a device to coordinate the transmissions among devices. In order to minimize the power consumption for the coordinator, we utilize the direction information extracted from beamformed transmissions in finding the coordinator automatically. The problem is formulated as a K-center problem, which is a NP-hard problem in general. Analysis is carried out to find optimal solutions in certain tractable topologies. Numerical algorithms and simulation results are further presented for random two dimensional topologies.