The solid-to-liquid phase transition in water nanofilms confined between plates, with varying separations and water plate interactions ranging from strongly hydrophobic to strongly hydrophilic, was simulated using a coarse-grained monatomic water model (mW) and the generalized replica exchange method (gREM). Extensive gREM simulations combined with the statistical temperature weighted histogram analysis method (ST-WHAM) provide a detailed description of the thermodynamic properties intrinsic to the phase transition, including the transition temperature, isobaric heat capacity, phase change enthalpy, entropy, and their dependence on the interplate distance and the plate water interaction. The ice structure of water nanofilms was characterized at various conditions using the transverse density profile and the distribution of angles formed by hydrogen-bonded neighboring molecules. Flat bilayer ice was observed to be the dominant solid phase at close interplate distance, while puckered bilayer ice, similar to a slab of ice Ih, is the predominant structure at larger interplates. Stable puckered bilayer ice, previously observed to have a low melting point, is observed to have enhanced stability with high melting temperature when confined between hydrophilic plates. These results demonstrate the strong dependence of phase stability and coexistence in nanoconfined systems on the geometry and physical properties of the confining environment.