It has been suggested that radio telescopes may be sensitive to axion dark matter that resonantly converts to radio photons in the magnetospheres surrounding neutron stars (NSs). In this work, we closely examine this possibility by calculating the radiated power from and projected sensitivity to axion dark matter conversion in ensembles of NSs within astrophysical systems like galaxies and globular clusters. We use population synthesis and evolution models to describe the spatial distributions of NSs within these systems and the distributions of NS properties. Focusing on three specific targets for illustration, the Galactic Center of the Milky Way, the globular cluster M54 in the Sagittarius dwarf galaxy, and the Andromeda galaxy, we show that narrow band radio observations with telescopes such as the Green Bank Telescope and the future Square Kilometer Array may be able to probe the quantum chromodynamics axion over roughly 2 orders of magnitude in mass, starting at a fraction of a micro-electron-volt.