In the powder bed fusion of metals using a laser beam (PBF-LB/M), an industrially highly relevant additive manufacturing technology, process parameters, such as the laser power, can be modified locally. This allows for a tailoring of the mechanical properties or a modification of the cracking susceptibility of the manufactured parts. That can be reasoned by the resulting microstructure, which in turn is strongly dependent on grain-initiating nucleation phenomena. Modeling the latter by means of numerical process simulations is, therefore, of high importance to widen the application area of PBF-LB/M. However, currently available nucleation models are either not able to represent the nucleation rates in PBF-LB/M or the models need to be calibrated for each process parameter set, which impedes a first-time-right additive manufacturing. The goal of this study was to adapt a classical nucleation model, which has proven to be a promising approach for PBF-LB/M microstructure simulations, to allow for a prediction of nucleation locations with varying process parameters and geometrical features. For this, various Inconel 718 specimens, expected to exhibit a geometry-related heat accumulation, were experimentally manufactured using different laser powers. The temperature behavior and the grain density were analyzed afterwards. The identical geometries were simulated by means of a finite element multi-scale simulation approach. A macro-scale simulation accounted for the geometrical features and provided the thermal boundaries to the meso-scale moving heat source simulation. The determined thermal values served as an input to the micro-scale simulation, represented by the adapted grain nucleation model. It was shown that the local and the global nucleation predictions agreed well with the experiments. Also, it was observed that the thermal gradient and the solidification rate need to be considered when modeling nucleation phenomena. These investigations contribute to a first-time-right manufacturing considering tailored microstructures and failure behavior in PBF-LB/M.