H-2 NMR of a liquid crystal confined to submicron cylindrical cavities, in a 17-K interval above the nematic-isotropic transition, reveals a weakly orientationally ordered molecular layer at the cavity wall governed by local interactions. The order (S0 = 0.02) is temperature independent so that a partial wetting is realized with no prewetting transition expected. A molecular exchange rate between the surface layer and the bulk is measured to be approximately 10(3) s-1. The coherence length measuring the order penetrating further into the cavity is described by alpha = 0.4 and xi-0 = 0.6 nm.