The change in site preference in NiAl(Ti,Cu) alloys with concentration is examined experimentally via ALCHEMI and theoretically using the Bozzolo-Ferrante-Smith (BFS) method for alloys. Results for the site occupancy of Ti and Cu additions as a function of concentration are determined experimentally for five alloys. These results are reproduced with large-scale BFS-based Monte Carlo atomistic simulations. The original set of five alloys is extended to 25 concentrations, which are modeled by means of the BFS method for alloys, showing in more detail the compositional range over which major changes in behavior occur. A simple but powerful approach based on the definition of atomic local environments also is introduced to describe energetically the interactions between the various elements and therefore to explain the observed behavior.