Venice High School, located at 13000 Venice  Boulevard, in the beachfront Los Angeles neighborhood of Venice, CA. (not far from the colorful Venice boardwalk) was used for exterior shots of the school buildings because it looked like a typical school from the 50's. 

The interior classroom scenes and the big dance contest were shot at Huntington Park High School (at 6020 Miles Ave, in Huntington Park, CA).

And the carnival scenes at the end of the movie were shot at John Marshall High School (at 3939 Tracy St., in the Los Feliz area of Los Angeles).