Zeolite synthesis using faujasite-type (FAU) zeolites as the starting silica/alumina source in the presence of various organic structure-directing agents (OSDAs) with cyclic alkylammonium structures was investigated. The obtained zeolite phases strongly depended on the structure of the OSDA and the Si/Al ratio of the starting FAU. Zeolites with different framework structures, such as BEA, MFI, CHA, and LEV, were obtained. Among the used OSDAs, methylpropylpyrrolidinium, butylmethylpyrrolidinium, and methylpropylpiperidinium effectively produced nanosized BEA and MFI zeolites, whereas dimethylpiperidinium and cyclohexyltrimethylammonium produced CHA and LEV zeolites, respectively. The nanosized MFI and BEA zeolites obtained through zeolite hydrothermal conversion exhibited remarkably smaller particle sizes and higher external surface area as compared to those of the conventional MFI and BEA zeolite samples synthesized using tetrapropylammonium and tetraethylammonium, respectively. We also found that the highly crystalline nanosized BEA and MFI zeolites exhibited better catalytic performance in the dehydration of benzyl alcohol to benzyl ether as compared to the conventional zeolites with large particle sizes. In addition, nanosized MFI zeolites, synthesized using FAU as a starting material and cyclic ammonium compounds, showed catalytic activities superior to those of the nanosized MFI zeolites synthesized from amorphous starting materials and cyclic ammonium compounds.