We evaluate the molecular response of hydration water as a function of temperature and proximity to the surface of the peptide N-acetyl-leucine-methylamide (NALMA) when in the presence of the kosmotrope co-solvent glycerol or the chaotrope co-solvent dimethyl sulfoxide (DMSO), using molecular dynamics simulation with a polarizable force field. These detailed microscopic studies complement established thermodynamic analysis on the role of co-solvents in shifting the equilibrium for proteins away from or towards the native folded state. We find that the structure of the water at the peptide interfaces reflects an increase in hydration number in the glycerol solution and a decrease in hydration numbers in the DMSO solution. While the water dynamics around NALMA in the presence of both co-solvents is slower than that observed with the water solvent alone, in the DMSO mixture we no longer measure a separation in water motion time scales at low temperatures as is seen in the pure water solvent, but rather one single relaxation time. In the glycerol, however, we do observe a separation of time scales at low temperatures, supporting the hypothesis that hydration water near a hydrophobic solute evolves on a separate time scale than the extensive hydrogen-bonding network of more bulk-like water. Our simulation studies highlight the differences in the two co-solvent solutions due to the relative frequency of water contacts with the hydrophobic vs. hydrophilic peptide surface, and direct water interactions with the co-solvents.