The structural and thermodynamic properties of a water droplet enclosed in a spherical cavity embedded in a hydrophobic material are studied. The structure of the interface between water and the hydrophobic material is analyzed as a function of cavity size, pressure, and the water-wall interaction potential. The propensity to form a density-enhanced (wet) or density-depleted (dry) interface is assessed by free-energy perturbation calculations. At high pressure, water wets the hydrophobic material, and at low pressure, the interface is dry. At ambient pressure, the specific equilibrium structure of the interface depends on the water-wall interaction potential. With a purely repulsive water-wall interaction potential, the water density at the interface is characteristic of a water-vapor interface (the dry state). The addition of dispersion attraction between water and the hydrophobic material causes notable structural changes; the width of the interface is reduced from approximately 4 Angstrom to less than 1 Angstrom, and the water droplet comes into contact with the wall. The water density at the wall, however, is depleted relative to the wet state. The results obtained in this work provide insights into the hydration properties of large hydrophobic molecular assemblies.