Polymer-coated nanoparticles (NP) are commonly used as drug carriers or theranostic agents. Their uptake rates are modulated by the interactions with essential serum proteins such as transferrin and albumin. Understanding the control parameters of these interactions is crucial for improving the efficiency of these nanoscale devices. In this work, we perform a multiscale computational study of protein adsorption onto polyethylene glycol (PEG) coated gold and silver NPs, producing protein-NP adsorption rankings as a function of PEG grafting density, which are validated against previously reported experimental protein-NP binding constants. Furthermore, the applied nano-docking method provides information on the preferred orientation of proteins immobilised on the surface of NPs. We propose a method of construction of model core-shell NPs in silico. The presented protocol can provide molecular level insights for the experimental development of biosensors, nanocarriers, or other nanoplatforms where information on the preferred orientation of protein at the bio-nano interface is crucial, and enables fast in silico prescreening of assays of various nanocarriers, i.e., combinations of proteins, NPs, and coatings.