The generation of high-order harmonics in solid crystals has received considerable attention recently. Using a driver laser with 0.8 µm wavelength and 28 fs ultrashort pulses, we present experimental results, accompanied with theoretical considerations, suggesting that the actual sources of the harmonics are nanometer-sized localized and transient electronic states on the surface of the materials when the laser intensity is in the non-perturbative regime. Adaptation of the bond model of the harmonic generation into the non-perturbative regime and including the quantum features of the process provide a localized excitation approach that correctly describes the measured polarization dependence of the harmonic signal, reflecting the microscopic surface structure and symmetries of the examined materials.