Your son might want to consider New Jersey Institute of Technology which is near NYC and would give him full tuition & fees if he becomes a NMF. There are all scholarships for honors students living in the dorms, too. I think there’s also a good bit of flexibility if he wanted to switch from engineering to CS or some other field.
If your son decides that he really isn’t interested in engineering, then I would also give strong consideration to DePaul in Chicago.
Perhaps @DadOfJerseyGirl might have some other suggestions?