Small numbers of nitrogen dopants dramatically modify the electronic properties of GaAs, generating spatially localized resonant states within the conduction band, pair and cluster states in the band gap, and very large shifts in the conduction-band energies with nonlinear concentration dependence. Cross-sectional scanning tunneling microscopy provides the local electronic structure of single nitrogen dopants at the (110) GaAs surface, yielding highly anisotropic spatial shapes when the empty states are imaged. Measurements of the resonant states relative to the GaAs surface states and their spatial extent allow an unambiguous assignment of specific features to nitrogen atoms at different depths below the cleaved (110) surface. Multiband tight-binding calculations around the resonance energy of nitrogen in the conduction band match the imaged features, verifying that the Green's function method can accurately describe the isolated isovalent nitrogen impurity. The spatial anisotropy is attributed to the tetrahedral symmetry of the bulk lattice and will lead to a directional dependence for the interaction of nitrogen atoms. Additionally, the voltage dependence of the electronic contrast for two features in the filled state imaging suggests these features could be related to a locally modified surface state.