Answer:
Lois Cowles Harrison Center for the Visual and Performing Arts in Lakeland, Fla. As just one example of its success, two graduates are currently on Broadway in "West Side Story" -- one as Anita and one as a member of the Sharks. Other grads have starred on Broadway or are enjoying success in music, acting or the visual arts or have gone on to unrelated careers after being educated at MIT, Princeton and other notable universities.
EDIT-I would have to say NOCCA(New Orleans Center for Creative Arts) Notable alumnus include multi-platinum and Grammy award winning artist Wynton Marsailas, 3 time Grammy winner Harry Connick Jr, Wendell Pierce known commonly as Det. Bunk Moreland on HBO's critically acclaimed series "The Wire", Anthony Mackie (Pap Doc in 8 Mile and Tupac in Notorious) as well as musicians Trombone Shorty, Terence Blanchard, Johnathan Batiste, and DJ Hollygrove. Many former NOCCA students have graduated from Julliard, Berkeley, Harvard, Princeton, Texas Southern University, LSU with B.A., Masters and Doctrines.
The above are the best schools in their local vicinity, however, it is widely accepted that the best school in the US for the performing arts, is Fiorello LaGuardia High School of the Arts. It was the school that the film Fame was based on. Notable alumni include Adrian Brody, Robert DeNiro, Jennifer Anniston, Al Pacino, Sarah Michelle Gellar, Ellen Barkin, Richard Benjamin, Laurence Fishburne, Dom DeLouise, and many many other award winning actors, singers, dancers, composers and artists. You can find out more information here: wiki/Fiorello_H._LaGuardia_High_School_of_Music_&_Art_and_Performing_Arts