Path integral Monte Carlo calculations of He-4 nanodroplets doped with alkali (Na+, K+ and Cs+) and alkali-earth (Be+ and Mg+) ions are presented. We study the system at T = 1 K and between 14 and 128 He-4 atoms. For all studied systems, we find that the ion is well localized at the center of the droplet with the formation of a "snowball" of well-defined shells of localized He-4 atoms forming solid-like order in at least the first surrounding shell. The number of surrounding helium shells (two or three) and the number of atoms per shell and the degree of localization of the helium atoms are sensitive to the type of ion. The number of He-4 atoms in the first shell varies from 12 for Na+ to 18 for Mg+ and depends weakly on the size of the droplet. The study of the density profile and of the angular correlations shows that the local solid-like order is more pronounced for the alkali ions with Na+ giving a very stable icosahedral order extending up to three shells.