The discovery of superconductivity in bilayer La₃Ni₂O₇ under pressure has sparked tremendous attention on Ruddlesden-Popper (RP) nickelates. Recently, a higher superconducting transition temperature of 96 K was reported in Sm-doped La₃Ni₂O₇ single crystals at ∼ 22 GPa. Motivated by this experimental observation, we systematically explore the crystal structure and electronic properties of La₃Ni₂O₇ doped with different rare-earth elements in comparison to the undoped counterpart. As expected due to the effect of chemical pressure, we find that the volume of La₂RNi₂O₇ (R= Pr, Nd, Sm) progressively decreases with doping from Pr to Sm. We further find a pressure-induced structural transition to tetragonal symmetry that approximately coincides with the emergence of superconductivity in all cases. This transition is characterized by the emergence of flat d_(z²) bands at the Fermi level in the electronic structure. Despite subtle distinctions in the electronic structure between undoped and R-doped La₃Ni₂O₇, an increase in the dominant planar hopping is obtained as the R size decreases. In contrast, the out-of-plane hopping decreases (in spite of the c lattice constant compression), due to the decrease in the apical Ni-O_(rm rocksalt) bond length. Our findings provide further microscopic insights into the effects of R-doping in the electronic structure of RP nickelate superconductors in connection to T_c.