IIRC, for most schools you'll have to audition with a specific set of pieces. An audition might look like this: A Bach P+F, an Etude (Chopin, Liszt, Rach or similar), a Beethoven/Mozart/Schubert Sonata, some Romantic composition (eg. Chopin Ballades or Scherzos) and another piece of your choice (maybe something more modern).
Juilliard being a prestigious school, I'd assume they expect you to play all of these very accurately and with a good musical interpretation. In other words, you'll have to play them all up to concert standard. They'll also probably want you to pick relatively hard pieces, so that means no op. 49 sonatas, no C minor prelude+fugue, etc.