A medium-long, but not fat nose with a small bump near the top. The bump also can't be too large, as if your nose has been broken. It is a term that can be applied to any distenguished facial feature. Having a Juliard nose means almost instant acceptance to Juliard University, or any other well-known performing arts college.
friend1--"Did you notice Chad's hair today? It's sticking up in the back."
friend2--"No, I was too busy looking at his fye Juliard Nose."
(E.g., Owen Wilson has a Juliard Nose)