The parent compounds of iron-based superconductors are magnetically ordered bad metals, with superconductivity appearing near a putative magnetic quantum critical point. The presence of both Hubbard repulsion and Hund's coupling leads to rich physics in these multiorbital systems, and motivated descriptions of magnetism in terms of itinerant electrons or localized spins. The NaFe1-xCuxAs series consists of magnetically ordered bad metal (x=0), superconducting (x≈0.02) and magnetically ordered semiconducing/insulating (x≈0.5) phases, providing a platform to investigate the connection between superconductivity, magnetism and electronic correlations. Here we use x-ray absorption spectroscopy and resonant inelastic x-ray scattering to study the valence state of Fe and spin dynamics in two NaFe1-xCuxAs compounds (x=0 and 0.47). We find that magnetism in both compounds arises from Fe2+ atoms, and exhibits underdamped dispersive spin waves in their respective ordered states. The dispersion of spin excitations in NaFe0.53Cu0.47As is consistent with being quasi-one-dimensional. Compared to NaFeAs, the band top of spin waves in NaFe0.53Cu0.47As is slightly softened with significantly more spectral weight of the spin excitations. Our results indicate the spin dynamics in NaFe0.53Cu0.47As arise from localized magnetic moments and suggest the iron-based superconductors are proximate to a correlated insulating state with localized iron moments.