Reduced graphene oxide (rGO) is one of the graphene derivatives that can be employed to engineer bioactive and/or electroactive scaffolds. However, the influence of its low and especially high concentrations on scaffolds’ overall properties and cytotoxicity has yet to be explored. In this study, polyethylene oxide (PEO)-based scaffolds containing from 0.1 to 20 wt% rGO were obtained by electrospinning. Morphological, thermal and electrical properties of the scaffolds were characterized by SEM, Raman spectroscopy, XRD, DSC and electrical measurements. The diameter of the fibers decreased from 0.52 to 0.19 µm as the concentration of rGO increased from 0.1 wt% to 20 wt%. The presence of rGO above the percolation threshold (5.7 wt%) resulted in a significantly reduced electrical resistivity of the scaffolds. XRD and Raman analysis revealed delamination of the graphene layers (interlayer spacing increased from 0.36 nm to 0.40–0.41 nm), and exfoliation of rGO was detected for the samples with an rGO concentration lower than 1 wt%. In addition, an evident trend of increasing cell viability as a function of the rGO concentration was evidenced. The obtained results can serve as further guidance for the judicious selection of the rGO content incorporated into the PEO matrix for constructing electroactive scaffolds.