In order to get better knowledge of mechanical properties from microscopic to macroscopic scale of biopolymers, viscoelastic bulk properties of aqueous solutions of sodium alginate were studied at different scales by combining macroscopic shear rheology (Hz), diffusing-wave spectroscopy microrheology (kHz-MHz) and Brillouin spectroscopy (GHz). Structural properties were also directly probed by small-angle X-ray scattering (SAXS). The results demonstrate a change from polyelectrolyte behavior to neutral polymer behavior by increasing polymer concentration with the determination of characteristic sizes (persistence length, correlation length). The viscoelastic properties probed at the phonon wavelength much higher than the ones obtained at low frequency reflect the variation of microscopic viscosity. First experiments obtained by metabolic activity assays with mouse embryonic fibroblasts showed biocompatibility of sodium alginate aqueous solutions in the studied range of concentrations (2.5-10 g L-1) and consequently their potential biomedical applications.