I have a question concerning boarding schools?

My daughter has recently taken an interest in the prospect of boarding houses/ schools. She seems to have fixed herself upon the idea. So I was wondering if perhaps anyone knew of a boarding school of some sort that might take profoundly gifted teenagers. I would prefer something more along the lines of a live in finishing school of some sort. My daughter is 14 and in the 10th grade, mind you she is not troubled in any way, and I am most certainly not looking for a disciplinary school of any sort. Thank you in advance for your answers.