Graphene-based frameworks suffer from a low quantum capacitance due to graphene’s Dirac point at the Fermi level. This theoretical study investigated the effect structural defects, nitrogen and boron doping, and surface epoxy/hydroxy groups have on the electronic structure and capacitance of graphene. Density functional theory calculations reveal that the lowest energy configurations for nitrogen or boron substitutional doping occur when the dopant atoms are segregated. This elucidates why the magnetic transition for nitrogen doping is experimentally only observed at higher doping levels. We also highlight that the lowest energy configuration for a single vacancy defect is magnetic. Joint density functional theory calculations show that the fixed band approximation becomes increasingly inaccurate for electrolytes with lower dielectric constants. The introduction of structural defects rather than nitrogen or boron substitutional doping, or the introduction of adatoms leads to the largest increase in density of states and capacitance around graphene’s Dirac point. However, the presence of adatoms or substitutional doping leads to a larger shift of the potential of zero charge away from graphene’s Dirac point.