A ZSM-5 fragment, containing 52 tetrahedral moieties, each of them formed by one silicon or one aluminum atom surrounded by four oxygen atoms, was employed to model (52T systems) by quantum chemical calculations (i) the influence of the positions of the acidic sites on the energetics of 22 aluminum monosubstituted and bisubstituted 52T acidic zeolite (H−ZSM-5) systems and (ii) the local adsorption properties and acidic strength of the corresponding −OH sites. The energetics and the structural properties of simpler acid H−ZSM-5 systems containing only five tetrahedral moieties (5T systems) were also modeled for comparison. B3LYP/6-31G(d,p) partial geometry optimization routines were performed on the 5T and 52T systems. On the latter, ONIOM(B3LYP/6-31G(d,p)|AM1) calculations and an alternative approach, i.e., the ONIOM method followed by a single-point at the above B3LYP/6-31G(d,p) level, aimed to decrease the need of computational resources, were also employed to analyze the properties of the different H−ZSM-5 models. The whole results showed that the orientation and the position of the acidic hydrogen atoms within the zeolite channel strongly affect the stability of the model systems, irrespective of the starting local topology characterizing the Al ↔ Si substitution site. Brönsted gas-phase acidity strength and adsorption-ability were evaluated through the analysis of the energy involved in (i) the proton dissociation from the acidic sites and (ii) the cis-but-2-ene and trans-but-2-ene adsorption on the same acidic sites. Both were affected, although to a very different extent, by the location and number of the considered −OH acidic groups. In particular, 2 among the 12 modeled acidic sites resulted in a highly stabilized zeolite structure, pointing out that the Al ↔ Si substitutions in the synthesis of aluminated ZSM-5 zeolites, and hence the corresponding catalytic activity, could preferentially occur on special sites. The choice of the computational method along with the size and the cutoff of the mimicked structures influenced the reliability of the calculations. The suggested alternative approach (that is, the ONIOM followed by the DFT single-point calculation) provided reasonable findings at very low computational cost.