As a parent of a Jazz Bass player who is about to graduate from NEC, I thought I would add my thoughts.
I was in a similar situation to you when our son applied in terms of my own knowledge about music and in regard to dealing with competing offers (although we had nothing as financially delicious as Purchase to consider because my son did not apply to any state schools).
So the first bit of advice I will give you is advice my son’s bass teacher told me. Looking back I think it was GREAT advice. The key to success in Jazz is not only who you study privately with, or what classes you take (ear training, theory etc…) it is finding opportunities to play with as many different people in as many different situations as you can. In other words putting yourself out there. So with that in mind ALL your choices are great. Purchase, Patterson and New School have access to NYC and NEC has the whole Boston scene.
The next thing to consider is what I call “soft factors”.
First what will make your son likely to build those connections and social groups so he has those opportunities to play in many different groups with many different people. And in that I suspect the four programs you list actually DO VARY. I can’t speak for the other three places (although I sort of know the New School). But I can speak to NEC because my son is there. Because NEC has a connection with Tufts and Harvard the students it attracts lean toward being a bit more academic and a bit more “nerdy” than maybe similar students at New School. That doesn’t mean they are better or worse musicians. It is just who they are. There are some students, like my son, who simply would not do well socially if he was not with other equally “nerdy” musicians. I suspect students at Purchase are probably going to be pretty academic as well, but I am not sure…I mostly say it because students I know personally who have gone to a CUNY or SUNY school have been very academically oriented.
Second where will your son be emotionally healthy. Obviously if your child is stressed about $$ or having to work excessively to afford travel home or if you can not afford to visit, those things can make him more anxious and depressed. If your son does not like the facilities, the practice rooms, the environment, the other students those things can make him depressed. I always tell parents to NOT DISCOUNT the value of being close to home. Kids get sick. They hit a bump and need to process something. They face a social dilemma. It is super valuable for a young 18-22 year old to go have a meal with mom and dad and work through things. It is hard to do over the phone and if travel is costly it might not occur as often as it is needed. I can’t tell you the number of times we have gotten a text from our son asking us to meet for brunch or dinner over the past four years. Those texts always give me a bit of a knot in my stomach as a mom. My brain immediately goes “What now?” And sometimes the things he is processing with us are big life questions about his career, what he is observing, what he is reading and how that impacts his thinking about his future. But other times it is little things such as I need help figuring out what summer program to apply to or questions about his living situation. 18 year olds are NOT ADULTS just yet and they still can benefit from more Mom and Dad time, especially if you have a good relationship with your child.
Third is a bit harder to think about but what about if your child decides he wants to not do music. Are there ways for him to explore or take other classes outside his music major. Are there opportunities to meet students who are not music majors. Who are those students? Are there clubs and other extra curricular activities that you can see your child being engaged in?
Finally the real decision should come down to your child. If he is NEC Or bust, then talk it out and be honest with him about what it means to have loans and how that might impact his graduate school choices. Also CALL NEC and talk to their financial people (who are excellent) and maybe explain that NEC is your son’s top choice BUT you have these other offers. You might be surprised what they come up with.