The burgeoning interest in the field of molecular magnetism is to perceive the high magnetic anisotropy in different geometries of metal complexes and hence to draw a magneto-structural correlation. Despite a handful of examples to exemplify the magnetic anisotropy in various coordination geometries of mononuclear complexes, the magnetic anisotropies for two different coordination geometries are underexplored. Employing an appropriate synthetic strategy utilizing the ligand LH2 [2,2'-{(1E,1'E)-pyridine2,6-diyl-bis(methaneylylidine)}-bis(azaneylylidine)diphenol] and cobalt halide salts in a 1 : 2 stoichiometric ratio in the presence of triethylamine allowed us to report a new family of dinuclear cobalt complexes [CoII2X2(L)(P)(Q)]·S with varying terminal halides [X = Cl, P = CH3CN, Q = H2O, S = H2O (1), X = Br, P = CH3CN, Q = H2O, S = H2O (2), X = I, P = CH3CN, and Q = CH3CN (3)]. All these complexes are characterized through single crystal X-ray crystallography, which reveals their crystallization in the monoclinic system P21/n space group with nearly identical structural features. These complexes share vital components, including Co(II) centers, a fully deprotonated ligand [L]2-, halide ions, and solvent molecules. The [L]2- ligand contains two Co(II) centers, where phenolate oxygen atoms bridge the Co(II) centers, forming a Co2O2 four-membered ring. Co1 demonstrates a distorted pentagonal-bipyramidal geometry with axial positions for solvent molecules, while Co2 displays a distorted tetrahedral geometry involving phenolate oxygen atoms and halide ions. Temperature-dependent dc magnetic susceptibility measurements were conducted on 1-3 within a range of 2 to 300 K at 1 kOe. The χmT vs. T plots exhibit similar trends, with χmT values at 300 K higher than the spin-only value, signifying a significant orbital contribution. As the temperature decreases, χmT decreases smoothly in all the complexes; however, no clear saturation at low temperatures is observed. Field-dependent magnetization measurements indicate a rapid increase below 20 kOe, with no hysteresis and a low magnetic blocking temperature. DFT and CASSCF/NEVPT2 theoretical calculations were performed to perceive the magnetic interaction and single-ion anisotropies of Co(II) ions in various ligand-field environments.