Mass spectra of helium nanodroplets doped with H2 and coronene feature anomalies in the ion abundance that reveal anomalies in the energetics of adsorption sites. The coronene monomer ion strongly adsorbs up to n = 38 H2 molecules indicating a commensurate solvation shell that preserves the D6h symmetry of the substrate. No such feature is seen in the abundance of the coronene dimer through tetramer complexed with H2; this observation rules out a vertical columnar structure. Instead we see evidence for a columnar structure in which adjacent coronenes are displaced in parallel, forming terraces that offer additional strong adsorption sites. The experimental value for the number of adsorption sites per terrace, approximately six, barely depends on the number of coronene molecules. The displacement estimated from this number exceeds the value reported in several theoretical studies of the bare, neutral coronene dimer.