  We present a new method for generating initial conditions for LCDM N-body
simulations which provides the dynamical range necessary to follow the
evolution and distribution of the fossils of the first galaxies on Local
Volume, 5-10 Mpc, scales. The initial distribution of particles represents the
position, velocity and mass distribution of the dark and luminous halos
extracted from pre-reionization simulations. We confirm previous results that
ultra-faint dwarfs have properties compatible with being well preserved fossils
of the first galaxies. However, because the brightest pre-reionization dwarfs
form preferentially in biased regions, they most likely merge into non-fossil
halos with circular velocities >20-30 km/s. Hence, we find that the maximum
luminosity of true-fossils in the Milky Way is L_V<10^5 L_solar, casting doubts
on the interpretation that some classical dSphs are true-fossils. In addition,
we argue that most ultra-faints at small galactocentric distance, R<50 kpc, had
their stellar properties modified by tides, while a large population of fossils
is still undetected due to their extremely low surface brightness log(Sigma_V)
< -1.4. We estimate that the region outside R_50 (~ 400 kpc) up to 1 Mpc from
the Milky Way contains about a hundred true fossils of the first galaxies with
V-band luminosities 10^3 - 10^5 L_solar and half-light radii, r_hl ~ 100-1000
pc.
