Protein hydration shell dynamics play an important role in biochemical processes including protein folding, enzyme function, and molecular recognition. We present here a comparison of the reorientation dynamics of individual water molecules within the hydration shell of a series of globular proteins: acetylcholinesterase, subtilisin Carlsberg, lysozyme, and ubiquitin. Molecular dynamics simulations and analytical models are used to access site-resolved information on hydration shell dynamics and to elucidate the molecular origins of the dynamical perturbation of hydration shell water relative to bulk water. We show that all four proteins have very similar hydration shell dynamics, despite their wide range of sizes and functions, and differing secondary structures. We demonstrate that this arises from the similar local surface topology and surface chemical composition of the four proteins, and that such local factors alone are sufficient to rationalize the hydration shell dynamics. We propose that these conclusions can be generalized to a wide range of globular proteins. We also show that protein conformational fluctuations induce a dynamical heterogeneity within the hydration layer. We finally address the effect of confinement on hydration shell dynamics via a site-resolved analysis and connect our results to experiments via the calculation of two-dimensional infrared spectra.