  We present FIRE/Gizmo hydrodynamic zoom-in simulations of isolated dark
matter halos, two each at the mass of classical dwarf galaxies ($M_{\rm vir}
\simeq 10^{10} M_{\odot}$) and ultra-faint galaxies ($M_{\rm vir} \simeq 10^9
M_{\odot}$), and with two feedback implementations. The resultant central
galaxies lie on an extrapolated abundance matching relation from $M_{\star}
\simeq 10^6$ to $10^4 M_{\odot}$ without a break. Every host is filled with
subhalos, many of which form stars. Our dwarfs with $M_{\star} \simeq 10^6
M_{\odot}$ each have 1-2 well-resolved satellites with $M_{\star} = 3-200
\times 10^3 M_{\odot}$. Even our isolated ultra-faint galaxies have
star-forming subhalos. If this is representative, dwarf galaxies throughout the
universe should commonly host tiny satellite galaxies of their own. We combine
our results with the ELVIS simulations to show that targeting $\sim 50~ \rm
kpc$ regions around nearby isolated dwarfs could increase the chances of
discovering ultra-faint galaxies by $\sim 35\%$ compared to random halo
pointings, and specifically identify the region around the Phoenix dwarf galaxy
as a good potential target.
  The well-resolved ultra-faint galaxies in our simulations ($M_{\star} \simeq
3 - 30 \times 10^3 M_{\odot}$) form within $M_{\rm peak} \simeq 0.5 - 3 \times
10^9 M_{\odot}$ halos. Each has a uniformly ancient stellar population ($ > 10~
\rm Gyr$) owing to reionization-related quenching. More massive systems, in
contrast, all have late-time star formation. Our results suggest that $M_{\rm
halo} \simeq 5 \times 10^9 M_{\odot}$ is a probable dividing line between halos
hosting reionization "fossils" and those hosting dwarfs that can continue to
form stars in isolation after reionization.
