We explore the excited state energy landscape of small polyhedral zinc sulfide clusters (Zn(4)S(4) and Zn(6)S(6)) using time-dependent density functional theory and correlated wave function based methods. We predict the optical absorption and photoluminescence spectra of the polyhedral clusters and demonstrate that, upon relaxation of the excited state, these nanostructures break symmetry and an electron and a hole localize on a small number of Zn (electron) and S (hole) centers. We further test several exchange-correlation potentials for their ability to recover the correlated wave function description of the excited state. Finally, we discuss how the degeneracy of excited states in nanostructures, such as those considered here, results in a Jahn-Teller distortion of the excited state geometry, and how numerical problems arising from this can be circumvented by starting the optimization of excited states from structures distorted along the ground state vibrational normal modes.