Molecular dynamics simulations were used to study properties of water at the interface with nanometer-size solutes. We simulated nonpolar attractive Kihara cavities given by a Lennard-Jones potential shifted by a core radius. The dipolar response of the hydration layer to a uniform electric field substantially exceeds that of the bulk. For strongly attractive solutes, the collective dynamics of the hydration layer become slow compared to bulk water, as the solute size is increased. The statistics of electric field fluctuations at the solute center are Gaussian and tend toward the dielectric continuum limit with increasing solute size. A dipolar probe placed at the center of the solute is sensitive neither to the polarity excess nor to the slowed dynamics of the hydration layer. A point dipole was introduced close to the solute-water interface to further study the statistics of electric field fluctuations generated by the water. For small dipole magnitudes, the free energy surface is single-welled, with approximately Gaussian statistics. When the dipole is increased, the free energy surface becomes double-welled, before landing in an excited state, characterized again by a single-welled surface. The intermediate region is fairly broad and is characterized by electrostatic fluctuations significantly in excess of the prediction of linear response. We simulated a solute having the geometry of C180 fullerene, with dipoles introduced on each carbon. For small dipole moments, the solvent response follows the results seen for a single dipole; but for larger dipole magnitudes, the fluctuations of the solute-solvent energy pass through a second maximum. The juxtaposition of the two transitions leads to an approximately cubic scaling of the chemical potential with the dipole strengh. Umbrella sampling techniques were used to generate free energy surfaces of the electric potential fluctuations at the heme iron in Cytochrome B562. The results were unfortunately inconclusive, as the ionic background was not effectively represented in the finite-size system.