The structure of the alanine hydration shell was modeled by Carr-Parinello molecular dynamics (CPMD) to explain subtle differences in NMR chemical shifts and indirect spin-spin coupling constants of the neutral (zwitterionic), cationic, and anionic forms of this amino acid. In comparison with classical molecular dynamics (MD), the quantum mechanical CPMD approach revealed a more structured solvent and significant differences in the radial and angular distributions of the water molecules around the solute. In particular, the solvent was predicted to be organized around the uncharged COOH and NH2 residues to a similar degree as that for the charged ones. This was not the case with MD. For snapshot CPMD configurations, the NMR parameters were computed by density functional theory (DFT) and averaged. Obtained values were significantly closer to experimental parameters known for N-15 and C-13 isotopically labeled alanine than those calculated by the conventional implicit dielectric solvent model. The NMR results also quantitatively reflect a superiority of the CPMD over the MD explicit solvent treatment. A further improvement of the computed spin-spin coupling constants could be achieved by taking into account vibrational averaging beyond the harmonic approximation. Differently positioned water molecules in the clusters cause an unexpectedly large scattering of the NMR parameters. About 10-15 dynamics snapshots were required for a satisfactory convergence of the shifts and couplings. The NMR chemical shift was found to be much more sensitive to the molecular hydration than the coupling. The results thus indicate a large potential of the NMR spectroscopy and quantum simulations to probe not only the structure of molecules but also their interactions with the environment.