Local variations in the work function of metal surfaces can arise from surface crystallographic orientation, grain-boundary termination, adsorbates, and structural defects. When these heterogeneous features coexist with finite spatial extents on a real surface, they can generate patch potentials and associated non-uniform stray electric fields. In this work, density functional theory (DFT) calculations are systematically performed to investigate how different types of structural and chemical heterogeneity affect the local electrostatic potential and work function of Au surfaces at the atomic scale. Three low-index surfaces, Au(100), Au(110), and Au(111), are first considered to elucidate how surface atomic arrangement and structural relaxation influence local potential variations. Surface grain boundaries, H, O, O₂, and OH· adsorbates, as well as surface vacancies, are then investigated to examine how localized structural and chemical perturbations modify the surface electrostatic environment. The results show that the clean Au(111) surface exhibits the smallest variation in work function among the three low-index surfaces, which is associated with its relatively high surface atomic density and more compact surface structure. In contrast, the lower surface atomic density and more pronounced structural relaxation of Au(110) make its surface electrostatic potential more sensitive to local structural changes. A distinct electrostatic potential difference is also found between regions near grain boundaries and the corresponding intragranular regions, suggesting that grain-boundary regions may contribute to local surface potential variations. For adsorbed species, the changes in work function are not determined solely by the net charge transfer quantified by Bader analysis. Instead, they arise from the combined effects of adsorption-induced charge redistribution, the associated dipole, and surface structural relaxation, demonstrating that net charge transfer alone is insufficient to characterize the electrostatic response of adsorbate-covered Au surfaces. Surface vacancies likewise induce localized changes in electron density and electrostatic potential within the defect region and the surrounding surface atoms. These results provide an atomic-scale picture of how surface crystallographic variations, structural defects, and chemical heterogeneities contribute to local potential variations on Au surfaces, thereby identifying possible microscopic origins of patch potentials. It should be emphasized that the present calculations describe idealized local structures under periodic boundary conditions rather than the full spatial characteristics of experimentally observed patch potentials. Therefore, quantitative prediction of the spatial distribution and electrostatic forces associated with realistic patch potentials requires further multiscale treatment incorporating patch size, spatial distribution, inter-electrode separation, surface morphology, and other realistic surface conditions.