The search for metal-free stars has so far been unsuccessful, proving that if
there are surviving stars from the first generation, they are rare, they have
been polluted, or we have been looking in the wrong place. To predict the
likely location of Population~III (Pop~III) survivors, we semi-analytically
model early star formation in progenitors of Milky Way-like galaxies and their
environments. We base our model on merger trees from the high-resolution dark
matter only simulation suite \textit{Caterpillar}. Radiative and chemical
feedback are taken into account self-consistently, based on the spatial
distribution of the haloes. Our results are consistent with the non-detection
of Pop III survivors in the Milky Way today. We find that possible surviving
Population III stars are more common in Milky Way satellites than in the main
Galaxy. In particular, low mass Milky Way satellites contain a much larger
fraction of Pop~III stars than the Milky Way. Such nearby, low mass Milky Way
satellites are promising targets for future attempts to find Pop~III survivors,
especially for high-resolution, high signal-to-noise spectroscopic
observations. We provide the probabilities for finding a Pop~III survivor in
the red giant branch phase for all known Milky Way satellites to guide future
observations.Comment: 17 pages, 12 figures, 1 table, submitted to MNRA