Dynamics of a coarse-grained model for the room-temperature ionic liquid, 1-ethyl-3-methylimidazolium hexafluorophosphate, couched in the united-atom site representation are studied via molecular dynamics simulations. The dynamically heterogeneous behavior of the model resembles that of fragile supercooled liquids. At or close to room temperature, the model ionic liquid exhibits slow dynamics, characterized by nonexponential structural relaxation and subdiffusive behavior. The structural relaxation time, closely related to the viscosity, shows a super-Arrhenius behavior. Local excitations, defined as displacement of an ion exceeding a threshold distance, are found to be mainly responsible for structural relaxation in the alternating structure of cations and anions. As the temperature is lowered, excitations become progressively more correlated. This results in the decoupling of exchange and persistence times, reflecting a violation of the Stokes-Einstein relation.