Scattering-type scanning near-field optical microscopy (s-SNOM) is currently regarded as a powerful tool for exploring important optical properties at nanoscale resolutions depending only on the size of a sharp tip that is scanned across the sample surface while being excited with a focused laser beam. Recently, it was shown that, among others, s-SNOM can quantitatively map the complex permittivity of materials and biological samples and hence other intrinsic related optical properties, such as the refractive index. In this work we apply this capability, previously demonstrated only at proof-of-concept level, in an experiment dealing with three distinct types of nanostructured materials: microcapsules for drug delivery assembled with layer-by-layer strategies, ultrathin optical coatings with controllable color properties, and plasmonic ceramic nanoparticles. We show that complex permittivity mapping with s-SNOM can contribute to the better understanding of such materials, providing information that is difficult or even impossible to assess with other techniques.