The muon hyperfine coupling constant (hfc) of the light hydrogen isotope muonium (Mu) was measured in aqueous methanol, NaCl, and KCl solutions with varying concentrations, in deuterated water, and in deuterated methanol. The muon hfc is shown to be sensitive to the size and composition of the primary solvation shell, and the three-dimensional harmonic oscillator model of Roduner et al. (J. Chem. Phys. 1995, 102, 5989) has been modified to account for dependence of the muon hfc on the methanol or salt concentration. The muon hfc of Mu in the aqueous methanol solutions decreases with increasing methanol concentration up to a mole fraction (χ_MeOH) of ~0.4, above which the muon hfc is approximately constant. The concentration dependence of the muon hfc is due to hydrophobic nature of Mu. It is preferentially solvated by the methyl group of methanol, and the proportion of methanol molecules in the primary solvation shell is greater than that in the bulk solution. Above χ_MeOH ~0.4, Mu is completely surrounded by methanol. The muon hfc decreases with increasing methanol concentration because more unpaired electron spin density is transferred from Mu to methanol than to water. The unpaired electron spin density is transferred from Mu to the solvent by collisions that stretch one of the solvents bonds. The amount of spin density transferred is likely inversely related to the activation barrier for abstraction from the solvent, which accounts for the larger muon hfc in the deuterated solvents. The muon hfc of Mu in electrolyte solution decreases with increasing concentration of NaCl or KCl. We suggest that the decrease of the muon hfc is due to the amount of spin density transferred from Mu to its surroundings being dependent on the average orientation of the water molecules in the primary solvation shell, which is influenced by both Mu and the ions in solution, and spin density transfer to the ions memselves.