The lattice site location of radioactive $^{27}$Mg implanted in AlN was determined by means of emission channeling. The majority of the $^{27}$Mg was found to substitute for Al, yet significant fractions (up to 33%) were also identified close to the octahedral interstitial site. The activation energy for interstitial Mg diffusion is estimated to be between 1.1 eV and 1.7 eV. Substitutional Mg is shown to occupy ideal Al sites within a 0.1 Å experimental uncertainty. We discuss the absence of significant displacements from ideal Al sites in the context of the current debate on Mg doped nitride semiconductors.