We present a study of the electronic properties of narrow zigzag and armchair nanoribbons substitutionally doped with a single boron, nitrogen, or phosphorus atom. Using density-functional calculations, we analyze the formation energy, electronic band structure, magnetic, and quantum conductance properties of these nanoribbons with doping sites ranging from the edge to the center of the ribbon. Substitutional doping is found to be most favorable at the ribbon edge in all the cases except for the boron-doped armchair ribbon, which has the lowest formation energy in the three-coordinated site next to the edge. Boron-doped zigzag nanoribbons exhibit spin-dependent donorlike states when the dopant is on the ribbon edge, and acceptor states as the dopant is moved toward the ribbon center. Nitrogen-doped zigzag nanoribbons show the opposite effect, while phosphorus-doped nanoribbons exhibit both donorlike and acceptorlike states. The band structure and local density of states indicate that dips in conductance occur from either the presence of a localized state or the opening of mini band gaps around a particular energy value. The variations in conductance arising from different doping profiles could be useful for tailoring the properties of graphene-based nanoelectronic devices.