We investigate theoretically the spatial dependence of the linear absorption spectra of single and coupledsemiconductor quantum dots, where the strong three-dimensional quantum confinement leads to an overallenhancement of Coulomb interaction and, in turn, to a pronounced renormalization of the excitonic properties.We show that—because of such Coulomb correlations and the spatial interference of the exciton wavefunctions—unexpected spectral features appear whose intensity depends on spatial resolution in a highlynonmonotonic way when the spatial resolution is comparable with the excitonic Bohr radius. We finallydiscuss how the optical near-field properties of double quantum dots are affected by their coupling.