Salting-out of hydrophobic solutes in aqueous salt solutions and their relevance to salt effects on biophysical phenomena are now well appreciated. Although salt effects on hydrophobic transfer have been well studied, to our knowledge, no quantitative molecular simulation study of salt-induced strengthening of hydrophobic interactions has yet been reported. Here we present quantitative characterization of salt-induced strengthening of hydrophobic interactions at the molecular and nanoscopic length scales through molecular dynamics simulations. Specifically, we quantify the effect of NaCl on the potential of mean force between molecular hydrophobic solutes (methanes) and on conformational equilibria of a 25-mer hydrophobic polymer that efficiently samples ensembles of compact and extended states in water. In both cases, we observe relative stabilization of compact conformations that is accompanied by a clear depletion of salt density (preferential exclusion) and a slight enhancement of water density (preferential hydration) in the solute vicinity. We show that the structural details of salt exclusion can be related to the salt-induced free energy changes using preferential interaction coefficients. We also test the applicability of surface-area-based models to describe the salt-induced free energy changes. These models provide a useful empirical description that can be used to predict the effects of salt on conformational equilibria of hydrophobic solutes. However, we find that the effective increase in the surface tension of the solute-aqueous solution interface depends on the type and concentration of salt as well as the length-scale (i.e., molecular vs nanoscopic) of the conformational change. These calculations underscore the utility of simulation studies to connect quantitatively structural details at the molecular level (described by preferential hydration/exclusion) to macroscopic solvation thermodynamics. The hydrophobic polymer also provides a useful model for studies of effect of thermodynamic variables (P, T, salt/additives) on many-body hydrophobic interactions at nanometer length scales.