We report a comprehensive Cu K-edge RIXS investigation of La2−xSrxCuO4 (LSCO) for 0≤x≤0.35, stripe-ordered La1.875Ba0.125CuO4 (LBCO), and La2Cu0.96Ni0.04O4 (LCNO) crystals. The RIXS spectra measured at three high-symmetry momentum transfer (q) positions are compared as a function of doping and for the different dopants. The spectra in the energy range 1-6 eV can be described with three broad peaks, which evolve systematically with increased doping. The most systematic trend was observed for q=(π, 0) corresponding to the zone boundary. As hole doping increased, the spectral weight transfer from high energies to low energies is nearly linear with x at this q. We interpret the peaks as interband transitions in the context of existing band models for this system, assigning them to Zhang-Rice band→upper Hubbard band, lower-lying band→upper Hubbard band, and lower-lying band→Zhang-Rice band transitions. The spectrum of stripe-ordered LBCO was also measured, and found to be identical to the correspondingly doped LSCO, except for a relative enhancement of the near-infrared peak intensity around 1.5-1.7 eV. The temperature dependence of this near-infrared peak in LBCO was more pronounced than for other parts of the spectrum, continuously decreasing in intensity as the temperature was raised from 25 K to 300 K. Finally, we find that 4% Ni substitution in the Cu site has a similar effect on the spectra as does Sr substitution in the La site.