We study the half-filled two-dimensional Hubbard model on a square lattice in cellular dynamical mean-field theory (CDMFT), a real-space cluster extension  of the dynamical mean-field theory. By increasing the number of cluster sites up to 6x6 we observe a progressive reduction of the onset interaction U* of a metal-insulator crossover. In particular, in the case of 4x4 sites, we observe a site-dependent U, which is lower at the center sites than at the corner sites. In addition to this real-space analysis we investigate different periodization schemes for the one-particle spectral function and argue that a center-focused  cumulant scheme is well-suited in the intermediate coupling regime of U due to its locality.
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