The optical properties of metallodielectric nanostructures, variations of a core-shell geometry, are investigated using the finite difference time domain method. This method provides a convenient, systematic, and general approach for calculating the optical response of a nanostructure of arbitrary symmetry and geometry to an incident light wave. Properties such as the optical absorption and scattering cross sections as well as the local electromagnetic fields and induced charge densities at the surfaces of the nanostructures can be obtained by this method. Issues of convergence with grid size and other simulation parameters are discussed in detail. The method is applied to uniform single nanoshells, nanoshells with surface defects, and nanoshells with shape distortions from a spherical geometry. The results show that, while defects can significantly affect local surface field enhancements, far field properties such as optical absorption and scattering spectra can be remarkably insensitive to defects and distortions.