Fabrication of a surface-engineered electrospun scaffold having biomimetic properties like the extracellular matrix (ECM) is essential for neural tissue engineering. An electroconductive and elastomeric scaffold with aligned fibers acting as a substrate may have a great impact on the directional outgrowth of neurites. In this study, we have electrospun electrically conductive, polyurethane-based elastomeric and topographically aligned fibro-porous neural scaffolds. Adhesive proteins of the ECM are documented to have an important role in controlling neuronal cell behavior, including cell adhesion, proliferation, and neurite outgrowth. These bio-adhesion proteins or nanomaterials mimicking their action, if used for surface modification of neural scaffolds, may have the potential to accelerate the nerve repair process. Thus, electrospun scaffolds fabricated were surface-engineered using a unique and modified single-step electrospraying technique to coat the scaffold surface with an exploratory bio-adhesion agent, a thin layer of graphene oxide (GO) films. The study was then carried out to determine if the GO-coated electrospun electroconductive polycarbonate urethane (PCU) substrate can improve the bio-interface attributes of these scaffolds or may alter the neurite outgrowth of PC-12 cells like any other bio-adhesion proteins. Therefore, the hybrid scaffolds with GO coatings were compared with similar scaffolds coated with poly-l-lysine (PLL) for neural cell adhesion, proliferation, and neurite extension. Neurite outgrowth studies showed that although the average neurite length was comparable on both GO- and PLL-coated surfaces, the length profile of neurites, when categorized based on length, showed an increased number of lengthier neurites on the GO-coated hybrid scaffolds. In particular, the study brings out an innovative surface engineering technique for the coating of GO on polymeric scaffolds. It may be further put together in designing of hybrid surfaces with nanotopographical biophysical cues on three-dimensional neural scaffolds, which in turn may stimulate an accelerated neuronal regeneration via providing an enhanced ECM like milieu.