Biocompatibility, biodegradability, shear tinning behavior, quick gelation and an easy crosslinking process makes alginate one of the most studied polysaccharides in the field of regenerative medicine. The main purpose of this study was to obtain tissue-like materials suitable for use in bone regeneration. In this respect, alginate and several types of clay were investigated as components of 3D-printing, nanocomposite inks. Using the extrusion-based nozzle, the nanocomposites inks were printed to obtain 3D multilayered scaffolds. To observe the behavior induced by each type of clay on alginate-based inks, rheology studies were performed on composite inks. The structure of the nanocomposites samples was examined using Fourier Transform Infrared Spectrometry and X-ray Diffraction (XRD), while the morphology of the 3D-printed scaffolds was evaluated using Electron Microscopy (SEM, TEM) and Micro-Computed Tomography (Micro-CT). The swelling and dissolvability of each composite scaffold in phosfate buffer solution were followed as function of time. Biological studies indicated that the cells grew in the presence of the alginate sample containing unmodified clay, and were able to proliferate and generate calcium deposits in MG-63 cells in the absence of specific signaling molecules. This study provides novel information on potential manufacturing methods for obtaining nanocomposite hydrogels suitable for 3D printing processes, as well as valuable information on the clay type selection for enabling accurate 3D-printed constructs. Moreover, this study constitutes the first comprehensive report related to the screening of several natural clays for the additive manufacturing of 3D constructs designed for bone reconstruction therapy.