We use cosmological simulations of isolated Milky Way-mass galaxies, as well as Local Group analogues, to define the edge -- a caustic manifested in a drop in density or radial velocity -- of Galactic-sized haloes, both in dark matter and in stars. In the dark matter, we typically identify two caustics: the outermost caustic located at ~1.4r_200m corresponding to the splashback radius, and a second caustic located at ~0.6r_200m which likely corresponds to the edge of the virialized material which has completed at least two pericentric passages. The splashback radius is ill defined in Local Group type environments where the halos of the two galaxies overlap. However, the second caustic is less affected by the presence of a companion, and is a more useful definition for the boundary of the Milky Way halo. Curiously, the stellar distribution also has a clearly defined caustic, which, in most cases, coincides with the second caustic of the dark matter. This can be identified in both radial density and radial velocity profiles, and should be measurable in future observational programmes. Finally, we show that the second caustic can also be identified in the phase-space distribution of dwarf galaxies in the Local Group. Using the current dwarf galaxy population, we predict the edge of the Milky Way halo to be 292 +/- 61 kpc.
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