The dynamics of water next to hydrophobic groups is critical for several fundamental biochemical processes such as protein folding and amyloid fiber aggregation. Some biomolecular systems, like melittin or other membrane-associated proteins, exhibit extended hydrophobic surfaces. Due to the strain these surfaces impose on the hydrogen (H)-bond network, the water molecules shift from the clathrate-like arrangement observed around small solutes to an anticlathrate-like geometry with some dangling OH bonds pointing toward the surface. Here we examine the water reorientation dynamics next to a model hydrophobic surface through molecular dynamics simulations and analytic modeling. We show that the water OH bonds lying next to the hydrophobic surface fall into two subensembles with distinct dynamical reorientation properties. The first is the OH bonds tangent to the surface; these exhibit a behavior similar to the water OHs around small hydrophobic solutes, i.e. with a moderate reorientational slowdown explained by an excluded volume effect due to the surface. The second is the dangling OHs pointing toward the surface: these are not engaged in any H-bond, reorient much faster than in the bulk, and exhibit an unusual anisotropy decay which becomes negative for delays of a few picoseconds. The H-bond dynamics, i.e. the exchanges between the different configurations, and the resulting anisotropy decays are analyzed within the analytic extended jump model. We also show that a recent spectroscopy technique, two-dimensional time resolved vibrational spectroscopy (2D-IR), can be used to selectively follow the dynamics of dangling OHs, since these are spectrally distinct from H-bonded ones. By computing the first 2D-IR spectra of water next to a hydrophobic surface, we establish a connection between the spectral dynamics and the dynamical properties that we obtain directly from the simulations.