The physisorption of water on graphene is investigated with the hybrid density functional theory (DFT)-functional B3LYP combined with empirical corrections, using moderate-sized basis sets such as 6-31G(d). This setup allows to model the interaction of water with graphene going beyond the quality of classical or semiclassical simulations, while still keeping the computational costs under control. Good agreement with respect to Coupled Cluster with singles and doubles excitations and perturbative triples (CCSD(T)) results is achieved for the adsorption of a single water molecule in a benchmark with two DFT-functionals (Perdew/Burke/Ernzerhof (PBE), B3LYP) and Grimme's empirical dispersion and counterpoise corrections. We apply the same setting to graphene supported by epitaxial hexagonal boron nitride (h-BN), leading to an increased interaction energy. To further demonstrate the achievement of the empirical corrections, we model, entirely from first principles, the electronic properties of graphene and graphene supported by h-BN covered with different amounts of water (one, 10 water molecules per cell and full coverage). The effect of h-BN on these properties turns out to be negligibly small, making it a good candidate for a substrate to grow graphene on.