Based on the analysis of 23 aluminum sites from 16 fluoroaluminates, the present work demonstrates the strong potential of combining accurate NMR quadrupolar parameter measurements, density functional theory (DFT)-based calculations of electric field gradients (EFG), and structure optimizations as implemented in the WIEN2k package for the structural and electronic characterizations of crystalline inorganic materials. Structure optimizations are essential for compounds whose structure was refined from usually less accurate powder diffraction data and provide a reliable assignment of the 27Al quadrupolar parameters to the aluminum sites in the studied compounds. The correlation between experimental and calculated EFG tensor elements leads to the proposition of a new value of the 27Al nuclear quadrupole moment Q(27Al) = 1.616 (±0.024) × 10-29 m2. The DFT calculations provide the orientation of the 27Al EFG tensors in the crystal frame. Electron density maps support that the magnitude and orientation of the 27Al EFG tensors in fluoroaluminates mainly result from the asymmetric distribution of the Al 3p orbital valence electrons. In most cases, the definition of relevant radial and angular distortion indices, relying on EFG orientation, allows correlations between these distortions and magnitude and sign of the Vii.