Molecular dynamics study of ionic liquids (ILs) is a challenging task. While accurate fully polarizable atomistic models exist, they are computationally too demanding for routine use. Most nonpolarizable atomistic models predict diffusion constants that are much lower than experiment. Scaled charge atomistic models are cost-effective and give good results for single component ILs but are in qualitative error for the phase behavior of mixtures, due to inaccurate prediction of the IL cohesive energy. In this work, we present an alternative approach for developing computationally efficient models that importantly preserves both the correct dynamics and cohesive energy of the IL. Employing a "top-down" approach, a hierarchy of coarse grained models for BMIM+EF4- are developed by systematically varying the polarization/atomic resolution of the distinct functional groups. Parametrization is based on symmetry-adapted perturbation theory (SAPT) calculations involving the homomolecular species; all cross interactions are obtained from mixing rules, and there are no adjustable parameters. We find that enhanced dynamics from a united-atom description counteracts the effect of reduced polarization, enabling computationally efficient models that exhibit quantitative agreement with experiment for both static and dynamic properties. We give explicit suggestions for reduced-description models that are computationally more efficient, more accurate, and more fundamentally sound than existing nonpolarizable atomistic models.