We present Gran Telescopio CANARIAS CanariCam 8.7 micron imaging and 7.5-13 micron spectroscopy of six local systems known to host an active galactic nucleus (AGN) and have nuclear star formation. Our main goal is to investigate whether the molecules responsible for the 11.3 micron polyclyclic aromatic hydrocarbon (PAH) feature are destroyed in the close vicinity of an AGN. We detect 11.3 micron PAH feature emission in the nuclear regions of the galaxies as well as extended PAH emission over a few hundred parsecs. The equivalent width (EW) of the feature shows a minimum at the nucleus but increases with increasing radial distances, reaching typical star-forming values a few hundred parsecs away from the nucleus. The reduced nuclear EW are interpreted as due to increased dilution from the AGN continuum rather than destruction of the PAH molecules. We conclude that at least those molecules responsible for the 11.3 micron PAH feature survive in the nuclear environments as close as 10 pc from the AGN and for Seyfert-like AGN luminosities. We propose that material in the dusty tori, nuclear gas disks, and/or host galaxies of AGN is likely to provide the column densities necessary to protect the PAH molecules from the AGN radiation field.