Well, I tried to suss out in my first post what the preferred budget numbers were, and although I agree that the college counselor at the boarding school would be the most helpful with respect to the student’s chances at the various colleges, I suspect that @ChoatieMom is likely correct that OP may not have cared for those suggestions and thus found his way here to get opinions from CC. My second list is filled with schools that would be likelier for admissions and significant merit aid and thus likely to hit whatever the unknown budget amount is.
I feel as though CC can be a place for a second opinion. It can be a way to confirm what the boarding school counselor said. Or it can be used to throw out some slightly more out-of-the-box ideas that could hit on something for the student (or just bounce off and fall to the ground). Of course, I’m one of those who tends to do exhaustive searches on possibilities to make sure there was no stone left unturned, and not everyone is like me in that respect. 