One- and two-photon excitation spectra of sodium atoms on the surface of helium droplets are reported. The spectra are recorded by monitoring the photoionization yield of desorbed atoms as function of excitation frequency. The excitation spectra involving states with principal quantum number up to n=6 can be reproduced by a pseudo-diatomic model where the helium droplet is treated as a single atom. For the lowest excited states of sodium, the effective interaction potentials for this system can be approximated by the sum of NaHe pair potentials. For the higher excited states, the interaction of the sodium valence electron with the helium induces significant configuration mixing leading to a failure of this approach. For these states, effective interactions potentials based on a perturbative treatment of the interactions between the valence electron, the alkali positive core and the helium, as described in detail in the accompanying publication, yield excellent agreement with experiment.