In this study, electrospun fiber scaffolds based on biodegradable and bioabsorbable polymers and showing a similar structure to that of the extracellular matrix (ECM) present in the neural tissues were prepared. The effects of electrospun-based scaffolds processed from poly(lactic acid) (PLA)/poly(lactide-b-ethylene glycol-b-lactide) block copolymer (PELA) and PLA/polyethylene glycol (PEG) (50:50 by wt) blends on the morphology, wettability, and mechanical properties, as well as on neural stem cell (NSC) behavior, were investigated. Thus, PLA/PELA and PLA/PEG fiber mats composed of PEG with different chain lengths were evaluated for optimal use as tissue engineering scaffolds. In both cases, the hydrophilic character of the scaffold surface was increased from the introduction of PEG homopolymer or PEG-based block copolymer compared with neat PLA. A microphase separation and a surface erosion of PLA/PEG blend-based electrospun fibers were highlighted, whereas PLA/PELA blend-based fibers displayed a moderate hydrophilic surface and a tunable balance between surface erosion and bulk degradation. Even if the mechanical properties of PLA fibers containing PEG or PELA decreased slightly, an excellent compromise between stiffness and the ability to sustain large deformation was found for PLA/PELA(2k), which displayed a significant increase in strain at break, that is, up to 500%. Our results suggest that both neat PLA and PLA/PELA blends supplemented with growth factors may mimic neural-like constructs and provide structural stability. Nonetheless, electrospun PLA/PELA blends have a suitable surface property, which may act synergistically in the modulation of biopotential for implantable scaffolding in neural tissue engineering.