Simulations of high-resolution F-19-decoupled Al-27 and Na-23 magic-angle spinning nuclear magnetic resonance (MAS NMR) spectra of the aluminofluoride minerals, cryolite, cryolithionite, thomsenolite, weberite, chiolite, prosopite, and ralstonite combined with theoretical modeling have given accurate values of chemical shift (delta(iso)), and quadrupolar interaction parameters (C-q and eta), thereby eliminating ambiguities incurred by the complex nuclear interactions. These NMR data have been correlated with local electronic environments in the minerals, which were calculated using Full Potential Linearized Augmented Plane Wave (FP LAPW) modeling based on the structures from X-ray diffraction (XRD) data. This combination of NMR, XRD, and modeling techniques allowed the analysis and optimization of the crystal structures. The electronegativities and distances of neighboring ions, represented here by an environmental parameter chi, are shown to control delta(iso) of both Na-23 and Al-27. The calculations using chi, also show that the ions beyond the nearest neighbor play an important role in determining delta(iso) of Al-27 and Na-23 in these aluminofluoride minerals, and the substitution of OH for F significantly affects the shielding around Al-27 in prosopite and ralstonite. There is a positive correlation between the site distortion at the Na and Al sites and the values of C-q in these aluminofluoride minerals.