Classical molecular dynamics (MD) simulations were used to investigate how free surfaces, as well as supporting substrates, affect phase separation in a NiAg alloy. Bulk samples, droplets, and droplets deposited on a graphene substrate were investigated at temperatures that spanned regions of interest in the bulk NiAg phase diagram, i.e., miscible and immiscible liquid, liquid-crystal, and crystal-crystal regions. Using MD simulations to cool down a bulk sample from 3000 K to 800 K, it was found that phase separation below 2400 K takes place in agreement with the phase diagram. When free surface effects were introduced, phase separation was accompanied by a core-shell transformation: spherical droplets created from the bulk samples became core-shell nanoparticles with a shell made mostly of Ag atoms and a core made of Ni atoms. When such droplets were deposited on a graphene substrate, the phase separation was accompanied by Ni layering at the graphene interface and Ag at the vacuum interface. Thus, it should be possible to create NiAg core-shell and layer-like nanostructures by quenching liquid NiAg samples on tailored substrates. Furthermore, interesting bimetallic nanoparticle morphologies might be tuned via control of the surface and interface energies and chemical instabilities of the system.