The binding interactions of six ligands, neutral and monocationic asymmetric monomethine cyanine dyes comprising benzoselenazolyl moiety with duplex DNA and RNA and G-quadruplex structures were evaluated using fluorescence, UV/Vis (thermal melting) and circular dichroism (CD) spectroscopy. The main objective was to assess the impact of different substituents (methyl vs. sulfopropyl vs. thiopropyl/thioethyl) on the nitrogen atom of the benzothiazolyl chromophore on various nucleic acid structures. The monomethine cyanine dyes with methyl substituents showed a 100-fold selectivity for G-quadruplex versus duplex DNA. Study results indicate that cyanines bind with G-quadruplex via end pi-pi stacking interactions and possible additional interactions with nucleobases/phosphate backbone of grooves or loop bases. Cyanine with thioethyl substituent distinguishes duplex DNA and RNA and G-quadruplex structures by distinctly varying ICD signals. Furthermore, cell viability assay reveals the submicromolar activity of cyanines with methyl substituents against all tested human cancer cell lines. Confocal microscopy analysis shows preferential accumulation of cyanines with sulfopropyl and thioethyl substituents in mitochondria and indicates localization of cyanines with methyl in nucleus, particularly nucleolus. This confirms the potential of examined cyanines as theranostic agents, possessing both fluorescent properties and cell viability inhibitory effect.