Hydrogel-supported neural cell cultures are more in vivo-relevant compared to monolayers formed on glass or plastic substrates. However, there is a lack of synthetic microenvironment available for obtaining standardized and easily reproducible cultures characterized by tissue-mimicking cell composition, cell–cell interactions, and functional networks. Synthetic peptides representing the biological properties of the extracellular matrix (ECM) proteins have been reported to promote the adhesion-driven differentiation and functional maturation of neural cells. Thus, such peptides can serve as building blocks for engineering a standardized, all-synthetic environment. In this study, we have compared the effect of two chemically crosslinked hydrogel compositions on primary cerebellar cells: collagen-like peptide (CLP), and CLP with an integrin-binding motif arginine-glycine-aspartate (CLP-RGD), both conjugated to polyethylene glycol molecular templates (PEG-CLP and PEG-CLP-RGD, respectively) and fabricated as self-supporting membranes. Both compositions promoted a spontaneous organization of primary cerebellar cells into tissue-like clusters with fast-rising Ca²⁺ signals in soma, reflecting action potential generation. Notably, neurons on PEG-CLP-RGD had more neurites and better synaptic efficiency compared to PEG-CLP. For comparison, poly-L-lysine-coated glass and plastic surfaces did not induce formation of such spontaneously active networks. Additionally, contrary to the hydrogel membranes, glass substrates functionalized with PEG-CLP and PEG-CLP-RGD did not sufficiently support cell attachment and, subsequently, did not promote functional cluster formation. These results indicate that not only chemical composition but also the hydrogel structure and viscoelasticity are essential for bioactive signaling. The synthetic strategy based on ECM-mimicking, multifunctional blocks in registry with chemical crosslinking for obtaining tissue-like mechanical properties is promising for the development of fast and well standardized functional in vitro neural models and new regenerative therapies.