In this work, we report on a detailed quantitative nanomechanical mapping of free-standing films of poly (ethylene terephthalate) (PET) and the composite PET/expanded graphite (EG) with 0.4% in weight of the nanoadditive, and of these materials nanostructured by laser irradiation. By using atomic force microscopy, we obtained simultaneously the topography, surface elastic modulus and adhesion force maps of the materials. Young's modulus images exhibited higher values for the composite in comparison to those of the neat polymer and for the nanostructured films in contrast to the non-nanostructured ones. Additionally, we explored the tribological properties of these systems at the nanoscale. Using lateral force microscopy, we observed a decrease in the friction coefficient for the nanocomposite as compared to the neat polymer, while quantifying an increase for both laser-structured samples. Our results are discussed taking into consideration the possible changes that the samples might undergo during processing, as well as the changes imposed by the complex geometry of the nanometric features in these laterally-resolved mechanical measurements.