A bio-inspired hydrogel for 3D bioprinting of soft free-standing neural tissues is presented. The novel filler-free bioinks were designed by combining natural polymers for extracellular matrix biomimicry with synthetic polymers to endow desirable rheological properties for 3D bioprinting. Crosslinking of thiolated Pluronic F-127 with dopamine-conjugated (DC) gelatin and DC hyaluronic acid through a thiol-catechol reaction resulted in thermally gelling bioinks with Herschel-Bulkley fluid rheological behavior. Microextrusion 3D bioprinting was used to fabricate free-standing cell-laden tissue constructs. The bioinks exhibited flattened parabolic velocity profiles with tunable low shear regions. Two pathways were investigated for curing the bioink: chelation and photocuring. The storage modulus of the cured bioinks ranged from 6.7 to 11.7 kPa. The iron (III) chelation chemistry produced crosslinked neural tissues of relatively lower storage modulus than the photocuring approach. In vitro cell viability studies using the 3D bioprinted neural tissues showed that the cured bioink was biocompatible based on minimal cytotoxic response observed over seven days in culture relative to control studies using alginate hydrogels. Rodent Schwann cell-, rodent neuronal cell-, and human glioma cell-laden tissue constructs were printed and cultured over seven days and exhibited comparable viability relative to alginate bioink controls. The ability to fabricate soft, free-standing 3D neural tissues with low modulus has implications in the biofabrication of microphysiological neural systems for disease modeling as well as neural tissues and innervated tissues for regenerative medicine.