How estimate E0-0 of an organic dye?
You're looking for the point where the normalized absorption and emission spectra cross each other.

The UV/Vis absorption spectra is almost always higher in energy (shorter wavelengths) than the emission spectra, because the molecule goes from the electronic and vibrational ground state to the electronic excited state. Usually this also means some vibrational modes are also excited. Since the molecule is typically in either the vibrational ground state or a low-energy vibrational state, the absorption process can go up several vibrational levels (i.e, the energy absorbed is higher than just the basic electronic excitation).

For emission, the molecule often loses some vibrational energy, so the emission comes from the ground vibrational state of that electronic excited state. The molecule ends up in the ground electronic state, but a vibrationally excited state (i.e., it loses a bit less energy than the $E_{0-0}$ energy difference).

So if you normalize the absorption and emission spectra, the crossing point should roughly correspond to the $E_{0-0}$ difference.