ZnO nanostructures were synthesized by a facile wet chemical method using water, ethanol and propanol as solvents. X-ray diffraction, field emission scanning electron microscopy (FESEM) and transmission electron microscopy (TEM) have been used to study the structural properties of the synthesized ZnO nanostructures, while their optical properties have been studied using UV-visible absorption spectroscopy and Raman spectroscopy. The photocatalytic activities of the as-synthesized ZnO nanostructures were evaluated by monitoring sunlight driven photocatalytic degradation of methylene blue (MB) and methyl orange (MO) dyes in water and it was observed that ZnO nanostructures prepared using propanol as a solvent exhibit highly enhanced photocatalytic activity as compared to those prepared using other solvents. The mechanism underlying the photocatalytic activity of ZnO nanostructures towards photocatalytic degradation of dyes is proposed. We attribute the highly enhanced photocatalytic activity of ZnO nanostructures prepared in propanol to the high surface area of nanosheets-like structures formed, which lead to enhanced adsorption of dye molecules resulting in efficient photocatalytic degradation of dyes upon sunlight irradiation.