By means of molecular dynamics simulations we study the structure and dynamics of water molecules in contact with a model hydrophobic surface: a planar graphene-like layer. The analysis of the distributions of a local structural index indicates that the water molecules proximal to the graphene layer are considerably more structured than the rest and, thus, than the bulk. This structuring effect is lost in a few angstroms and is basically independent of temperature for a range studied comprising parts of both the normal liquid and supercooled states (240K to 320K). In turn, such structured water molecules present a dynamics that is slower than the bulk, as a consequence of their improved interactions with their first neighbors.