Mechanical properties of materials are highly dependent on microstructure. One characteristic example is tensile stresses at the grain boundaries, which is one of the most critical factors in crack nucleation. Although experimental techniques have significantly evolved during the past decades with respect to obtaining high-resolution snapshots of the microstructure with methods such as scanning electron microscopy, the quantitative estimation of continuum quantities, such as localized stresses, still remains a very challenging task. The molecular dynamics simulation method has been proven to be a quite effective simulation tool for providing insights in such challenges due to its high spatial and temporal resolution. In this study, molecular dynamics simulations have been performed to obtain a spatial resolution of the residual stresses in solidified aluminum. A best-effort realistic microstructure was obtained by starting from a pure aluminum block which was initially melted and subsequently quenched under various cooling rates, and finally relaxed. The obtained results suggest that residual stresses are higher in absolute terms at the vicinity of grain boundaries than at the grain interiors, and higher crystallinity has been found to be correlated to lower residual stresses. Moreover, it has been shown both qualitatively and quantitatively that grain boundaries undergo tensile loading, in contrast to the grain interiors which are compressed; this result comes to support the conclusions of quite recent experimental investigations, showing that the residual stress is tensile at the grain boundaries and gradually transits into compressive in the grain interiors, and highlights the potential of molecular dynamics simulation to capture nanoscale physical phenomena.