This paper presents the synthesis of the organic–inorganic hybrid perovskite, CH3NH3PbI3, doped in the Pb2+ position with Sn2+, Sr2+, Cd2+ and Ca2+. The incorporation of the dopants into the crystalline structure was analysed, observing how the characteristics of the dopant affected properties such as the crystalline phase, emission and optical properties. XRD showed how doping with Sn2+, Sr2+ and Cd2+ did not modify the normal tetragonal phase. When doping with Ca2+, the cubic phase was obtained. Moreover, DR-UV-Vis spectroscopy showed how the band gap decreased with the dopants, the values following the trend Sr2+ < Cd2+ < Ca2+ < CH3NH3PbI3 ≈ Sn2+. The biggest decrease was generated by Sr2+, which reduced the CH3NH3PbI3 value by 4.5%. In turn, cathodoluminescence (CL) measurements confirmed the band gap obtained. Periodic-DFT calculations were performed to understand the experimental structures. The DOS analysis confirmed the experimental results obtained using UV-Vis spectroscopy, with the values calculated following the trend Sn2+ ≈ Pb2+ > Cd2+ > Sr2+ for the tetragonal structure and Pb2+ > Ca2+ for the cubic phase. The electron localization function (ELF) analysis showed similar electron localizations for undoped and Sn2+-doped tetragonal structures, which were different from those doped with Sr2+ and Cd2+. Furthermore, when Cd2+ was incorporated, the Cd–I interaction was strengthened. For Ca2+ doping, the Ca–I interaction had a greater ionic nature than Cd–I. Finally, an analysis based on the non-covalent interaction (NCI) index is presented to determine the weak-type interactions of the CH3NH3 groups with the dopant and I atoms. To our knowledge, this kind of analysis with these hybrid systems has not been performed previously.