The adsorption of benzene on the Cu(111), Ag(111), Au(111), and Cu(110) surfaces at low coverage is modeled using density-functional theory (DFT) using periodic-slab models of the surfaces as well as using both DFT and complete-active-space self-consistent field theory with second-order Møller-Plesset perturbation corrections (CASPT2) for the interaction of benzene with a Cu13 cluster model for the Cu(110) surface. For the binding to the (111) surfaces, key qualitative features of the results such as weak physisorption, the relative orientation of the adsorbate on the surface, and surface potential changes are in good agreement with experimental findings. Also, the binding to Cu(110) is predicted to be much stronger than that to Cu(111) and much weaker than that seen in previous calculations for Ni(110), as observed. However, a range of physisorptive-like and chemisorptive-like structures are found for benzene on Cu(110) that are roughly consistent with observed spectroscopic data, with these structures differing dramatically in geometry but trivially in energy. For all systems, the bonding is found to be purely dispersive in nature with minimal covalent character. As dispersive energies are reproduced very poorly by DFT, the calculated binding energies are found to dramatically underestimate the observed ones, while CASPT2 calculations indicate that there is no binding at the Hartree-Fock level and demonstrate that the expected intermolecular correlation (dispersive) energy is of the correct order to explain the experimental binding-energy data. DFT calculations performed for benzene on Cu(110) and for benzene on the model cluster indicate that this cluster is actually too reactive and provides a poor chemical model for the system.