In recent years, numerous studies highlighted the crucial role of the soil–structure interaction (SSI) in the seismic performance of basement structures. However, there remains a limited understanding of how this interaction affects buildings with basement structures under varying site conditions. Based on the three-dimensional (3D) numerical analysis method, the influence of the SSI on the seismic response of high-rise steel frame–core wall (SFCW) structures situated on shallow-box foundations were investigated in this study. To further investigate the effects of the SSI and site conditions, three types of soil profiles—soft, medium, and hard—were considered, along with a fixed-foundation model. The results were compared in terms of the maximum lateral displacement, inter-story drift ratio (IDR), acceleration amplification coefficient, and tensile damage for the SFCW structure under different site conditions, with both fixed-base and shallow-box foundation configurations. The findings highlight that the site conditions significantly affected the seismic performance of the SFCW structure, particularly in the soft soil, which increased the lateral deflection and inter-story drift. Moreover, compared with non-pulse-like ground motion, pulse-like ground motion resulted in a higher acceleration amplification coefficient and greater structural response in the SFCW structure. The RC core wall–basement slab junction was a critical region of stress concentration that exhibited a high sensitivity to the site conditions. Additionally, the maximum IDRs showed a more significant variation at incidence angles between 20 and 30 degrees, with a more pronounced effect at a seismic input intensity of 0.3 g than at 0.2 g.