In this work, extensive molecular dynamics simulations of mixtures of alcohols of several chain lengths (methanol and ethanol) with the ionic liquids (ILs) composed of the cation 1-hexyl-3-methylimidazolium and several anions of different hydrophobicity degrees (Cl(-), BF(4)(-), PF(6)(-)) are reported. We analyze the influence of the nature of the anion, the length of the molecular chain of the alcohol, and the alcohol concentration on the thermodynamic and structural properties of the mixtures. Densities, excess molar volumes, total and partial radial distribution functions, coordination numbers, and hydrogen bond degrees are reported and analyzed for mixtures of the ILs with methanol and ethanol. The aggregation process is shown to be highly dependent on the nature of the anion and the size of the alcohol, since alcohol molecules tend to interact predominantly with the anionic part of the IL, especially in mixtures of the halogenated IL with methanol. Particularly, our results suggest that the formation of an apolar network similar to that previously reported in mixtures of ILs with water does not take place in mixtures with alcohol when the chloride anion is present, the alcohol molecules being instead homogeneously distributed in the polar network of IL. Moreover, the alcohol clusters formed in mixtures of [HMIM][PF(6)] with alcohol were found to have a smaller size than in mixtures with water. Additionally, we provide a semiquantitative analysis of the dependence of the hydrogen bonding degree of the mixtures on the alcohol concentration.