The excessive use of antibiotics has contributed to the rise in antibiotic-resistant bacteria, and thus, new antibacterial compounds must be developed. Composite materials based on graphene and its derivatives doped with metallic and metallic oxide nanoparticles, particularly Ag, Cu, and Cu oxides, hold great promise. These materials are often modified with polyethylene glycol (PEG) to improve their pharmacokinetic behavior and their solubility in biological media. In this work, we performed molecular dynamics (MD) simulations to study the interaction between small Ag, Cu, and CuO clusters and several graphene-based materials. These materials include pristine graphene (PG) and pristine graphene nanoplatelets (PGN) as well as PEGylated graphene oxide (GO_PEG) and PEGylated graphene oxide nanoplatelets (GO-PEG_N). We calculated the adsorption energies, mean equilibrium distances between the nanoparticles and graphene surfaces, and mean square displacement (MSD) of the nanoclusters. The results show that PEGylation favors the adsorption of the clusters on the graphene surfaces, causing an increase in adsorption energies and a decrease in both distances and MSD values. The strengthening of the interaction could be crucial to obtain effective antibacterial compounds.