Electronic properties of nanostructured graphene are determined in the framework of a third nearest neighbour mean field Hubbard model. Band gaps and magnetic ground states of 0D graphene flakes, 1D graphene nanoribbons and 2D triangular graphene antidots with hexagonal holes are considered. Structures with sublattice imbalance are found to be ferromagnetic, while for balanced sublattices we identify a critical size above which the ground state is antiferromagnetic. The antiferromagnetic ground state increases the band gap, giving large band gaps with a profound effect on the optical response. Finally, we examine the stability of the antiferromagnetic states for increased temperature and doping. We find the structures to depolarize for T ∼ 1000 K and doping ∼ 1% impurities.