Yale does not have a performance major, minor or concentration. Princeton has a performance concentration. Yale’s study of music is academic, but you can take lessons with grad students, and occasionally, if you’re at a very high level, with a professor from The School of Music. However, Yale does have a ton of music ensembles and lots of very good musicians as undergrads.
As for public university programs - if finances are an issue you’ll want to apply in your home state, or ones which have reasonable out of state fees. And then you’ll need to check if non music majors can participate in the top orchestras or if they’re reserved for those in the School of Music. (Such as at Michigan, UCLA or Indiana - all of which have very good music programs and are public.) Again, you really should be asking these questions on the Music Major forum, even if you don’t plan to major in music.