We present Feedback in Realistic Environment (FIRE)/GIZMO hydrodynamic zoom-in simulations of isolated dark matter haloes, two each at the mass of classical dwarf galaxies (Mvir ≃ 1010 M o˙) and ultra-faint galaxies (Mvir ≃ 109 M o˙), and with two feedback implementations. The resulting central galaxies lie on an extrapolated abundance matching relation from M* ≃ 106 to 104 M o˙ without a break. Every host is filled with subhaloes, many of which form stars. Each of our dwarfs with M* ≃ 106 M o˙ has 1-2 well-resolved satellites with M* = 3-200 × 103 M o˙. Even our isolated ultra-faint galaxies have star-forming subhaloes. If this is representative, dwarf galaxies throughout the Universe should commonly host tiny satellite galaxies of their own. We combine our results with the Exploring the Local Volume in Simulations (ELVIS) simulations to show that targeting ~50 kpc regions around nearby isolated dwarfs could increase the chances of discovering ultra-faint galaxies by ~35 per cent compared to random 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* ≃ 3-30 × 103 M o˙) form within Mpeak ≃ 0.5-3 × 109 M o˙ haloes. Each has a uniformly ancient stellar population (>10 Gyr) owing to reionization-related quenching. More massive systems, in contrast, all have late-time star formation. Our results suggest that Mhalo ≃ 5 × 109 M o˙ is a probable dividing line between haloes hosting reionization 'fossils' and those hosting dwarfs that can continue to form stars in isolation after reionization