We report Cu-63 and Cu-65 NMR on Cu2Se, a superionic conductor of interest for thermoelectric and other applications. Results demonstrate an initial appearance of ionic hopping in a narrow temperature range above 100 K, coinciding with the recently observed low-temperature phase transition. At room temperature and above, this goes over to rapid Cu-ion hopping and a single motionally narrowed line both above and below the alpha-beta structural transition. The low-temperature alpha' phase exhibits a sizable metallic shift, in contrast to the high-temperature structures. The large variation in native carrier density, significantly enhanced at positions associated with Cu vacancies, indicates the strong influence of an impurity band on low-temperature electronic transport.