Methods for promoting and controlling the differentiation of human mesenchymal stem cells (hMSCs) in vitro before in vivo transplantation are crucial for the advancement of tissue engineering and regenerative medicine. In this study, we developed poly(ethylene glycol) diacrylate (PEGDA) hydrogels with tunable mechanical properties, including elasticity and viscoelasticity, coupled with bioactivity achieved through the immobilization of a mixture of RGD and a mimetic peptide of the BMP-2 protein. Despite the key relevance of hydrogel mechanical properties for cell culture, a standard for its characterization has not been proposed, and comparisons between studies are challenging due to the different techniques employed. Here, a comprehensive approach was employed to characterize the elasticity and viscoelasticity of these hydrogels, integrating compression testing, rheology, and atomic force microscopy (AFM) microindentation. Distinct mechanical behaviors were observed across different PEGDA compositions, and some consistent trends across multiple techniques were identified. Using a photoactivated cross-linker, we controlled the functionalization density independently of the mechanical properties. X-ray photoelectrin spectroscopy and fluorescence microscopy were employed to evaluate the functionalization density of the materials before the culturing of hMSCs on them. The cells cultured on all functionalized hydrogels expressed an early osteoblast marker (Runx2) after 2 weeks, even in the absence of a differentiation-inducing medium compared to our controls. Additionally, after only 1 week of culture with osteogenic differentiation medium, cells showed accelerated differentiation, with clear morphological differences observed among cells in the different conditions. Notably, cells on stiff but stress-relaxing hydrogels exhibited an overexpression of the osteocyte marker E11. This suggests that the combination of the functionalization procedure with the mechanical properties of the hydrogel provides a potent approach to promoting the osteogenic differentiation of hMSCs.