Pulsed field gradient (PFG) NMR in combination with quasielastic neutron scattering (QENS) was used to investigate self-diffusion of water and acetone in Nafion membranes with and without immobilized vanillic acid (VA). Complementary characterization of these membranes was performed by small angle X-ray scattering (SAXS) and NMR relaxometry. This study was motivated by the recent data showing that an organic acid, such as VA, in Nafion can preserve its catalytic activity in the presence of water even at high intra-polymer water concentrations corresponding up to 100% ambient relative humidity. However, there is currently no clear understanding of how immobilized organic acid molecules influence the microscopic transport properties and related structural properties of Nafion. Microscopic diffusion data measured by PFG NMR and QENS are compared for Nafion with and without VA. For displacements smaller than the micrometer-sized domains previously reported for Nafion, the VA addition was not observed to lead to any significant changes in the water and/or acetone self-diffusivity measured by each technique inside Nafion. However, the reported PFG NMR data present evidence of a different influence of acetone concentration in the membranes with and without VA on the water permeance of the interfaces between neighboring micrometer-sized domains. The reported diffusion data are correlated with the results of SAXS structural characterization and NMR relaxation data for water and acetone.