We examine the crystal structures and magnetic properties of several S = 1 Ni(II) coordination compounds, molecules and polymers, that include the bridging ligands HF^-₂, AF^2-₆ (A = Ti, Zr) and pyrazine or non-bridging ligands F^-, SiF^2-₆, glycine, H₂O, 1-vinylimidazole, 4-methylpyrazole and 3-hydroxypyridine. Pseudo-octahedral NiN₄F₂, NiN₄O₂ or NiN₄OF cores consist of equatorial Ni-N bonds that are equal to or slightly longer than the axial Ni-L_ax bonds. By design, the zero-field splitting (D) is large in these systems and, in the presence of substantial exchange interactions (J), can be difficult to discriminate from magnetometry measurements on powder samples. Thus, we relied on pulsed-field magnetization in those cases and employed electron-spin resonance (ESR) to confirm D when J ≪ D. The anisotropy of each compound was found to be easy-plane (D > 0) and range from ≈ 8-25 K. This work reveals a linear correlation between the ratio d(Ni-L_ax)/d(Ni-N_eq) and D although the ligand spectrochemical properties may play an important role. We assert that this relationship allows us to predict the type of magnetocrystalline anisotropy in tailored Ni(II) quantum magnets.