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 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 signalto-noise spectroscopic observations. We provide the probabilities of finding a Pop III survivor in the red giant branch phase for all known Milky Way satellites to guide future observations.