In this work, two novel zigzag one–dimensional Co(II) and Cu(II) coordination polymers (CP1 and CP2) derived from 2,5–dihydroxyterephthalic acid and 2,2'–bipyridine ligands were synthesized and characterized by multispectroscopic (UV–vis, FTIR, EPR, sc–XRD) and analytical techniques. Single crystal X–ray diffraction studies revealed a monoclinic crystal system with I2/a and P2₁/m space group for CP1 and CP2, respectively. The DFT studies were performed to study the structural and electronic properties of CP1 and CP2 and the results revealed that HOMO electron density was localized around the central metal ions whereas, LUMO electron density is diffused throughout the polymeric structures and was mostly localized on 2,2'–bipyridine ligand. Additionally, the Hirshfeld studies analysis was carried out to study the various intra–/intermolecular interactions that stabilize the crystal structure and our results showed that CP1 and CP2 were majorly stabilized by H‒H interactions. The chemotherapeutic efficacy of CP1 and CP2 were explored by studying the in vitro DNA binding interactions utilizing multispectroscopic techniques including UV−visible, fluorescence, circular dichroism and cyclic voltammetry. The synthesized coordination polymers were also evaluated for their biosensing activity and the finding revealed that CP1 showed selective sensing for levofloxacin (LVF) whereas, CP2 proved to be an efficient sensor for chloramphenicol (CLAM), LVF and nitrofurantoin (NFT). We have further evaluated the catechol oxidase activity of CP1 and CP2 was assessed by using 3,5−DTBC as a potential substrate. The chemotherapeutic potential of CP1 and CP2 was ascertained by carrying out in vitro cytotoxic activity against neuroblastoma (SH–SY5Y) cell line employing cisplatin as a reference and the results displayed better anticancer activity of CP2 which was evident from their IC₅₀ values.