Monte Carlo simulations of the organization of charged anisotropic colloids are performed to illustrate the possible electrostatic origin of the microsegregation and the flocculation recently detected for aqueous suspensions of Laponite clay. In the framework of a hierarchical approach, the long-range electrostatic coupling is treated by a multipole expansion. A set a simulation biases (cavity, orientation, and Rosenbluth samplings) are used to improve the acceptance ratio of the particle displacements. The potential of mean force, obtained from the ratio of the radial distribution functions calculated for charged and neutral platelets, exhibits an attraction resulting from the electrostatic coupling only.