Efficient Monte Carlo simulations are used to determine the liquid liquid binodal line of mixtures of hard-sphere colloids and neutral polymers under good-solvent conditions for two values of the polymer-to-colloid size ratio q, q = 0.5 and 1. We use a multiblob coarse-graining approach, in which groups of monomers are mapped onto a single pseudoatom (a blob) and blob-blob interactions are obtained by requiring the model to reproduce some large-scale properties of the polymer solution in the dilute limit. We also compute several experimentally relevant quantities at a few selected points along the binodal: thermodynamic properties (pressure, isothermal compressibility, chemical potentials), partial structure factors, and polymer form factor. Finally, we discuss how the polymers become more compact with increasing colloidal crowding.