Methods to decouple epitaxial graphene from metal substrates have been extensively studied, with anticipation of observing unperturbed Dirac cone properties, but its local electronic structures were rarely studied. Here, we investigated the local variations of Dirac cones recovered using oxygen intercalation applied to epitaxial graphene on Ru(0001) using scanning tunneling microscopy and spectroscopy (STM and STS). New V-shaped features, which appear in the STS data at the oxygen-intercalated graphene regions, are attributed to the signatures of recovered Dirac cones. The Dirac point energy was observed at 0.48 eV below the Fermi level, different from previous photoemission results because of different oxygen coverages. The observed spatial variations of Dirac point energy were explained by the weakly protruding network structures caused by a small net strain in graphene. Our study shows that oxygen-intercalated graphene provides an excellent platform for further graphene research at the nano-meter scale with unperturbed Dirac cones.