The study of how molecules adsorb, diffuse, interact, and desorb from imperfect surfaces is essential for a complete understanding of elementary surface processes under relevant pressure and temperature conditions. Here we use first-principles calculations to study the adsorption of benzene and naphthalene on a vicinal Cu(443) surface with the aim to gain insight into the behavior of aromatic hydrocarbons on realistic surfaces at a finite temperature. Upon strong adsorption at step edges at a low temperature, the molecules then migrate from the step to the (111) terraces, where they can freely diffuse parallel to the step edge. This migration happens at temperatures well below the onset of desorption, suggesting a more complex dynamical picture than previously proposed from temperature-programed desorption studies. The increase of the adsorption strength observed in experiments for Cu(443) when compared to Cu (111) is explained by a stronger long-range van der Waals attraction between the hydrocarbons and the step edges of the Cu(443) surface. Our calculations highlight the need for time-resolved experimental studies to fully understand the dynamics of molecular layers on surfaces.