With increasing interest in new catalytic materials based on doping of cerium dioxide with other metal cations, it is necessary to have an atomic level understanding of the factors that impact on the structural and electronic properties of doped ceria as well as its reactivity. We present in this paper simulations of the ceria (111) and (110) surfaces doped with divalent cations Pd and Ni using density functional theory (DFT) corrected for on-site Coulomb interactions (DFT + U) and hybrid DFT (using the screened exchange HSE06 functional). Structural distortions due to doping are strong in both surfaces and the most stable structure for both dopants arises through compensation of the dopant + 2 valence through oxygen vacancy formation. Both dopants also lower the formation energy of the active oxygen vacancy in each surface, confirming the potential for these dopants to be used in ceria based materials for catalysis or solid oxide fuel cells, where the oxygen vacancy formation energy is important. When comparing DFT + U and hybrid DFT, although the qualitative descriptions provided by both DFT approaches are similar, we do find that the energetics of oxygen vacancy formation are quantitatively different and the importance of this point is discussed.