CsSnI3 is a potential lead-free inorganic perovskite for solar energy applications due to its nontoxicity and attractive optoelectronic properties. Despite these advantages, photovoltaic cells using CsSnI3 have not been successful to date, in part due to low stability. We demonstrate how gradual substitution of Rb for Cs influences the structural, thermodynamic, and electronic properties on the basis of first-principles density functional theory calculations. By examining the effect of the Rb:Cs ratio, we reveal a correlation between octahedral distortion and band gap, including spin-orbit coupling. We further highlight the cation-induced variation of the ionization potential (work function) and the importance of surface termination for tin-based halide perovskites for engineering high-performance solar cells.