Doping oxide materials by inserting atoms of a different element in their lattices is a common procedure for modifying properties of the host oxide. Using catalytically active, yet expensive noble metals as dopants allows synthesizing materials with atomically dispersed metal atoms, which can become cost-efficient catalysts. The stability and chemical properties of the resulting materials depend on the structure of the host oxide and on the position of the dopant atoms in it. In the present work we analyze by means of density functional calculations the relative stability and redox properties of cerium dioxide (ceria) nanoparticles doped with atoms of four technologically relevant transition metals - Pt, Pd, Ni and Cu. Our calculations indicate that the dopants are most stable at surface positions of ceria nanoparticles, highlighting the role of under-coordinated sites in the preparation and characterization of doped nanostructured oxides. The energies of two catalytically important reduction reactions - the formation of oxygen vacancies and homolytic dissociative adsorption of H2 - are found to strongly depend on the position of the doping atoms in nanoparticulate ceria.