In this work, extensive molecular dynamics simulations of the dynamics of mixtures of ionic liquids (ILs) composed of the cation 1-hexyl-3-methylimidazolium and several anions of different hydrophobicity degrees (Cl(-), BF(4)(-), PF(6)(-)) with alcohols of different chain lengths (methanol and ethanol) are reported. We evaluated the influence of the nature of the anion, the length of the molecular chain of the alcohol, and the alcohol concentration on some dynamical properties of the mixtures, such as self-diffusion coefficients of all the species, mean square displacements (with an analysis of both ballistic and diffusive regimes), and velocity autocorrelation functions of alcohol molecules. The diffusivity of the mixtures was found to be highly dependent on the nature of the anion since the interaction between chloride and alcohols is greater than that with fluorinated anions and leads to slower dynamics. Additionally, our results show that self-diffusion coefficients increase with alcohol concentration. On the other hand, a subdiffusive regime over thousands of picoseconds was detected at intermediate times through analysis of the center-of-mass mean square displacements of alcohol molecules, a region that becomes narrower as alcohol concentration increases. Finally, the study of the role of the anion and of solvent concentration on velocity autocorrelation functions reflects an increase in mean collision times as the amount of alcohol increases until the value of pure alcohols is reached. These collision times are smaller in mixtures with halogenated ILs.