Using first-principles calculations, we identify "tune-out" optical wavelengths, lambda(zero), for which the ground-state frequency-dependent polarizabilities of alkali-metal atoms vanish. Our approach uses high-precision, relativistic all-order method in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. We discuss the use of tune-out wavelengths for sympathetic cooling in two-species mixtures of alkali metals with group II and other elements of interest. Special cases in which these wavelengths coincide with strong resonance transitions in a target system are identified.