Through exponential sample-size scaling of conductance, we demonstrate strong electron localization in three sets of nanostructured antidot graphene samples with localization lengths of 1.1, 2, and 3.4 μm. The large-scale mesoscopic transport is manifest as a parallel conduction channel to 2D variable range hopping, with a Coulomb quasigap around the Fermi level. The opening of the correlation quasigap, observable below 25 K through the temperature dependence of conductance, makes possible the exponential suppression of inelastic electron-electron scatterings and thereby leads to an observed dephasing length of 10 μm.