I also forgot to ask do you want to be a big fish in a small pond or small fish in a big pond. It's important that you figure out how you respond to certain educational situations: do you need lots of one on one attention or are you pretty self sufficient? Are you motivated or intimidated by people who are better than you. There are no right or wrong answers to these questions but they are vital for finding you the perfect fit. When you say you want to major in music, have you thought more specifically about that? Meaning if you want cutting edge jazz you'll need NYC influence. If you want studio work then an L.A. based school might be up your alley. Education majors might take a different turn. I don't mean to be difficult I'm trying to answer your question specifically and not just rattle off schools that have good programs. Larger schools with well known programs include: North Texas, Indiana, NEC, Eastman, William Patterson and Miami to name a few. Smaller schools might include University of Cincinnati, University of Louisville, Julliard. Another element to consider is the type of jazz you want to excel in. Again this is about you- I would advise different schools for different styles: bebop, post-bop, smooth jazz, pop/fusion, etc... Finally I would stress a school that has a well-known saxophone educator ( not just well-known player). I don't mean to insult some of my colleagues but with the music industry changing many famous players are turning to the financial stability of the education system. The universities are happy to have them because their names draw students. However not all of them are great teachers, and even more importantly they have very lenient schedules. They may go on the road for 2 months and then cram in 6 of your private lessons in 3 days. That won't benefit you at all. These are important questions to ask of possible teachers.