Poly-ε-caprolactone (PCL) has been widely used in additive manufacturing for the construction of scaffolds for bone tissue engineering. However, its use is limited by its lack of bioactivity and inability to induce cell adhesion, hence limiting bone tissue regeneration. Biomimicry is strongly influenced by the dynamics of cell-substrate interaction. Thus, characterizing scaffolds at the cell scale could help to better understand the relationship between surface mechanics and biological response. We conducted atomic force microscopy-based nanoindentation on 3D-printed PCL fibers of ~300 µm thickness and mapped the near-surface Young's modulus at loading forces below 50 nN. In this non-disruptive regime, force mapping did not show clear patterns in the spatial distribution of moduli or a relationship with the topographic asperities within a given region. Remarkably, we found that the average modulus increased linearly with the logarithm of the strain rate. Finally, a dependence of the moduli on the history of nanoindentation was demonstrated on locations of repeated nanoindentations, likely due to creep phenomena capable of hindering viscoelasticity. Our findings can contribute to the rational design of scaffolds for bone regeneration that are capable of inducing cell adhesion and proliferation. The methodologies described are potentially applicable to various tissue-engineered biopolymers.