We are entering an era in which we will be able to detect and characterize hundreds of dwarf galaxies within the Local Volume. It is already known that a strong dichotomy exists in the gas content and star formation properties of field dwarf galaxies versus satellite dwarfs of larger galaxies. In this work, we study the more subtle differences that may be detectable in galaxies as a function of distance from a massive galaxy, such as the Milky Way. We compare smoothed particle hydrodynamic simulations of dwarf galaxies formed in a Local Volume-like environment (several megaparsecs away from a massive galaxy) to those formed nearer to Milky Way–mass halos. We find that the impact of environment on dwarf galaxies extends even beyond the immediate region surrounding Milky Way–mass halos. Even before being accreted as satellites, dwarf galaxies near a Milky Way–mass halo tend to have higher stellar masses for their halo mass than more isolated galaxies. Dwarf galaxies in high-density environments also tend to grow faster and form their stars earlier. We show observational predictions that demonstrate how these trends manifest in lower quenching rates, higher H i fractions, and bluer colors for more isolated dwarf galaxies.