We study transport length scales in carbon nanotubes and graphene ribbons under the influence of Anderson disorder. We present generalized analytical expressions for the density of states, the elastic mean free path and the localization length in arbitrarily structured quantum wires. These allow us to analyze the electrical response near the van Hove singularities and in particular around the edge state in graphene nanoribbons. Comparing with the results of numerical simulations, we demonstrate that both the diffusive and the localized regime are well represented by the analytical approximations over a wide range of the energy spectrum. In graphene nanoribbons, we find that the zigzag edge state causes a strong reduction of the localization length in a wide energy range around the Fermi energy.