Scattering-type scanning near-field optical microscopy (SNOM) offers the possibility to analyze material properties like strain in crystals at the nanoscale. In this paper we introduce a SNOM setup employing a newly developed tunable broadband laser source with a covered spectral range from 9 µm to 16 µm. This setup allows for the first time optical analyses of the crystal structure of gallium nitride (GaN) at the nanometer scale by excitation of a near-field phonon resonance around 14.5 µm. On the example of an artificially induced stress field within a GaN wafer, we present a method for a 2D visualization of small deviations in the crystal structure, which allows for fast qualitative characterizations. Subsequently, the stress levels at chosen points were quantified by recording complex near-field spectra and correlating them with theoretical model calculations. Applied to the cross-section of a heteroepitaxially grown GaN wafer, we finally demonstrate the capability of our setup to analyze the relaxation of the crystal structure along the growth axis with a nanometer spatial resolution.