X-ray absorption is the standard method to probe the unoccupied density of states at a given edge. Here we show that polarized resonant inelastic x-ray scattering in La2CuO4 at the Cu L edge is extremely sensitive to the environment of the Cu atom and the fine structure in the Cu 4p density of states. Combined ab initio and many-body cluster calculations, used for the first time in such a context, show remarkable agreement with experiment. In particular, we identify a nonlocal effect, namely, a transition to off-site Cu 3d states.