We present a strategy for direct numerical simulations of nucleate boiling on three-dimensional unstructured grids, enabling the representation of complex geometries. The method relies on a ghost fluid formulation with two temperature fields and two velocity fields, one for each phase. Sharp discontinuities are enforced at the interface for pressure, temperature, and velocity. Numerical methods with third-order spatial accuracy are used for the temperature field and for interface curvature evaluation. We also introduce a new level-set reinitialization procedure accounting for the presence of a contact line, which allows the accurate imposition of the contact angle for bubbles and droplets on a surface. The phase-change solver is first assessed against reference cases of rising bubbles and film boiling. Three-dimensional simulations of nucleate boiling of water are then performed and compared with the results of [15,21], obtained on structured two-dimensional axisymmetric grids. Finally, nucleate boiling on a complex geometry, namely an artificial nucleation site, is simulated. The results compare favorably with the experiments of [38]. Overall, this strategy enables three-dimensional direct numerical simulations of nucleate boiling on unstructured grids and complex geometries.