Nonresonant inelastic x-ray scattering measurements on NiO and CoO show that strong dipole-forbidden d-d excitations appear within the Mott gap at large wave vectors. These dominant excitations are highly anisotropic, and have [001] nodal directions for NiO. Theoretical analyses based on a novel, energy-resolved Wannier function (within the local density approximation+Hubbard U) show that the anisotropy reflects the local exciton wave functions and local point-group symmetry. The sensitivity to weak symmetry breaking in particle-hole wave functions suggests a wide application to strongly correlated systems.