Identification of the novel (E)-N′-((2-chloro-7-methoxyquinolin-3-yl)methylene)-3-(phenylthio)propanehydrazide scaffold 18 has led to the development of a new series of biologically active hydrazide compounds. The parent compound 18 and new quinoline derivatives 19–26 were prepared from the corresponding quinoline hydrazones and substituted carboxylic acids using EDC-mediated peptide coupling reactions. Further modification of the parent compound 18 was achieved by replacement of the quinoline moiety with other aromatic systems. All the newly synthesized compounds were evaluated for their anti-cancer activity against the SH-SY5Y and Kelly neuroblastoma cell lines, as well as the MDA-MB-231 and MCF-7 breast adenocarcinoma cell lines. Analogues 19 and 22 significantly reduced the cell viability of neuroblastoma cancer cells with micromolar potency and significant selectivity over normal cells. The quinoline hydrazide 22 also induced G1 cell cycle arrest, as well as upregulation of the p27kip1 cell cycle regulating protein.