A good hydrogen storage material should adsorb hydrogen in high concentrations and with optimal binding energies. Exohedrally metal decorated carbon fullerene structures were proposed as a promising material in this context. We present a fully ab-initio, unbiased structure search of the configurational space of decorated C60 fullerenes and find that many of the hitherto postulated ground state structures are not ground states. We determine the energetically lowest configurations for decorations with a varying number of decorating atoms (2 ≤ n ≤ 32) for alkali metals, alkaline-earth metals as well as some other important elements and find that the dense uniform distribution of the decorating atoms over the surface of the C60 , desired for hydrogen storage, can be obtained only for a few elements. An understanding of the behavior of the decorating atoms can be obtained by analyzing their bonding characteristics via the electron localization function.