Direct-write extrusion bioprinting, a form of additive manufacturing, is a useful technique to recapitulate anatomical complexity for tissue engineering applications. However, bioprinting has hit a bottleneck in progress due to the lack of available bioinks with high printability, mechanical strength, and biocompatibility. Here, we report a family of hydrogel-based bioinks for extrusion bioprinting from poly (ethylene glycol) (PEG) and two-dimensional (2D) nanoparticles. PEG, a non-fouling easily modifiable polymer, combined with biocompatible Laponite XLG nanoparticles (2D nanosilicates) to obtain shear-thinning hydrogel bioinks. Electrostatic interactions between nanoparticles and hydrogen-bonding between polymer and nanoparticles govern the flow behavior and printability of bioink. The evaluation of hydrogel bioink using flow sweeps, peak holds, and dynamic oscillatory rheology, suggest that minimum shear-thinning index of ~0.3, solution viscosities >1000 Pa.s, and 80% recovery within 30s are necessary for printing high fidelity constructs. Mechanically stiff 3D printed structures are obtained by covalently crosslinking polymeric chains using ultraviolet (UV) light. Modifications to the PEG system through inclusion of dithiothreitol linkage or combining with gelatin methacrylate are used to control matrix degradation, cell adhesion properties, and therapeutic release. We envision that PEG bioinks can be used to print complex, large-scale, cell-laden tissue constructs with high structural fidelity and mechanical stiffness for applications in custom bioprinted scaffolds and tissue engineered implants.