For me:
1)Cost. Obviously if family finances allow paying full freight then this isn’t a consideration, but it should be a big factor. Is it worth going to the school that has the big name and the big teacher if it is going to leave the kid with huge debt? No. I have heard people say it is, because in going to the prestige school/teacher, the likelyhood of getting a well paid gig is higher, that could allow paying off the debt,and that is simply not true. Kids coming out of the premiere schools don’t routinely jump out of there and get into a high level orchestra or into well paying positions. Yes there are exceptions, you hear about the kid at Northwestern who jumped into the Chicago symphony before they graduated , kid from Curtis going into the Philly, but that is a rarity. I just can’t see a kid graduating from music school with the intent of pursuing music as a career with a load of debt.
2)If cost is no concern, then teacher would be next. People have debated this but music teaching is a very personal relationship, if the student and teacher don’t click, it can be rough, and if the teacher, who may be great with some kids isn’t a match, it will be tough. Obviously going to an affordable school where the teaching on the instrument isn’t good is not going to work well either.
3)Prestige (though I wouldn’t use that term). Strength of student body and networking opportunities are very real, but the name of the school is not magic in music in of itself. If you come out of Juilliard or Curtis or NEC, that name isn’t going to get you jobs by itself. However, being around other high level students can drive a music student forward, and there is networking among music students and in a higher level program you can make friends or play with other students and end up forming a group for example, or find out about opportunities.
4)Location. That is a tricky one, is that being located so kids can see high level music events like let’s say living in NYC and seeing the NY Phil? Is it for the idea of being able to do gigs while in school, for example a jazz student who might be able to find gigs in the local area, or become known to groups or bookers in the area? I would have to say this really depends on what the location can do for the student. Obviously there is the environment itself, being in a city like New York or Boston is very different than being at a school in a more rural area, it all depends on the kids and what motivates them. I know someone who went to U Mich for music because they wanted the college experience with Saturday going to the football game and being in a university setting.
5)Campus, safety and weather I would put at the bottom personally. Lot of great music schools are in areas that can have bad weather. Lot of great schools have been located in areas that some consider safety risks (when my brother went to Columbia U many decades ago, the areas bordering the school were not great). Most of the time with safety to be honest the dangers are overstated because the school is in a city area.
Beautiful Campus/Buildings is nice to have, but for example when my son went to NEC the buildings were nothing to write home about and there really wasn’t a campus (though of course being in the area it is in, Back Bay, it it was a nice area).