This work studies graphene on nanostructured ionic substrates using density functional theory (DFT) and the density functional tight binding (DFTB). Flat ionic substrates can provide graphene with a mechanical support without compromising its electronic properties, while the nanostructures can modify the electron behaviour in graphene sheets and potentially create devices such as on-sheet junctions. Previous to the calculations, we extend the self-consistent charge DFTB method (SCC-DFTB) to a self-consistent charge and dipole DFTB scheme (SCCD-DFTB), which allows atomic dipoles to be considered self-consistently. This new scheme is implemented and its parametrisation discussed. Assessment is made based upon calculations of some electronic properties of Carbon-based systems including fullerenes, nanotubes and graphenes. Studies of graphene on ionic substrates confirm that flat ionic substrates do not influence the electronic structure of graphene in the vicinity of Dirac points. In the case of nanostructured surfaces, it is identified that steps or pits with divalent impurity and cation vacancy pair with possible relaxations are the key to introducing sizeable electrostatic potential variations on graphene layers that can cause changes of the electronic structures of graphene at the low energy range recently observed in experiments.