We present a computational study of individual and pairs of substitutional Mn impurities on the (110) surface of GaAs samples based on density functional theory. We focus on the anisotropy properties of these magnetic centers and their dependence on on-site correlations, spin-orbit interaction, and surface-induced symmetry-breaking effects. For a Mn impurity on the surface, the associated acceptor-hole wave function tends to be more localized around the Mn than for an impurity in bulk GaAs. The magnetic anisotropy energy for isolated Mn impurities is of the order of 1 meV, and can be related to the anisotropy of the orbital magnetic moment of the Mn acceptor hole. Typically Mn pairs have their spin magnetic moments parallel aligned, with an exchange energy that strongly depends on the pair orientation on the surface. The spin magnetic moment and exchange energies for these magnetic entities are not significantly modified by the spin-orbit interaction, but are more sensitive to on-site correlations. Correlations in general reduce the magnetic anisotropy for most of the ferromagnetic Mn pairs.