We show that self-ordered anodic aluminum oxide containing hexagonal arrays of cylindrical nanopores with submicron periodicity is a versatile model system for the exploration of rich phononic phenomena at gigahertz frequencies, which are intimately linked to fluids located in the nanopores and their interactions with the pore walls. Using high-resolution Brillouin spectroscopy we report the first realization of directional flow of elastic energy parallel and perpendicular to the pore axes, phonon localization, and tunability of the phononic band structure.