We have investigated the spectral properties of Fe impurities in a Cs host, for both surface and bulk systems, by means of a combination of density functional theory in the local density approximation and dynamical mean-field theory (LDA + DMFT). The effective impurity model arising in LDA + DMFT was solved via two different techniques, i.e., the Hubbard I approximation and the exact diagonalization. It is shown that noticeable differences can be seen in the unoccupied part of the spectrum for different positions of Fe atoms in the host, despite the fact that hybridization between Fe d-states and Cs is low. Our calculations show good agreement with the experimental photoemission spectra reported by Carbone et al. [Carbone, Veronese, Moras, Gardonio, Grazioli, Zhou, Rader, Varykhalov, Krull, Balashov, Mugarza, Gambardella, Lebègue, Eriksson, Katsnelson, and Lichtenstein, Phys. Rev. Lett. 104, 117601 (2010)].