Understanding the adsorption properties of organic molecules on graphene-based substrates is important for such applications as air and water filters. Pristine graphene is often the model substrate used in the theoretical investigations of this problem. While useful, pristine single-layer graphene is however an idealized model. In this work, we assess the effect of the presence of point defects (single vacancy, divacancy, and the Stone-Wales defect) in single-layer and bilayer graphene on the energetics of adsorption of benzene and toluene. Our calculations benchmark three different dispersion-corrected DFT schemes, namely PBE-D2, vdW-DF1, and vdW-DF2-C09. Whereas the presence of the single vacancy and the double vacancy does not appear to alter the adsorption energies of the aromatic molecules by an appreciable amount, the Stone-Wales defect and the addition of a second graphene layer stabilizes their interaction with the substrate by several tens of meV.