My response, edited for this post:
Whew! Top 5 grad schools? That's going to be difficult to answer. It's also hard to talk about because my training as an undergraduate and masters student does not make this list. So I will make the following conversation easier by offering the caveat that there are amazing institutions of higher learning across the country beyond this narrow list. Fantastic musicians often come from unlikely places, and half of what is interesting to people is the life story of the person, and often that means the more unique the story the better. And in the case of smaller schools, who doesn't love a good Cinderella story? That being said, I will now don my elitist hat and give you what you've asked for:
If we're limited only to US Conservatories:
Eastman
Juilliard
Mannes
Manhattan
Peabody
San Francisco
If we're talking about only Universities with excellent graduate music programs:
Indiana
UNT
UT
USC
UCLA
UMich
I would posit that there is value to looking for "Brand-name" cachet, but you also absolutely need to be at a place where you can have a great relationship with the teacher with whom you want to study. Ideally, you want a place that has both. Juilliard is the best name brand simply because it is the most internationally well known institution of music, perhaps now better-known than any one particular conservatory in Europe. This much is a reality independent of the quality of the instruction or the outcomes for students attending. So even if individual programs are stronger at other places, more people not in the music business will know and respect your credentials. This is useful for some musicians more than it is for others, depending on your concentration. Peabody is a very strong name brand that is made even better because it is now the Peabody Conservatory of the Johns Hopkins University, and so you widen the net of folks who will instantly respect you. If they don't know much about one of America's oldest conservatories, they absolutely will be familiar with Johns Hopkins.
In the case of composition: I can say, as a panelist for composition competitions, that we adjudicators do unavoidably look at resumes and consider a composer's training as a factor. It doesn't decide who wins, and we do choose people from "dark horse" schools, but it does help you to get promoted out of the pile, into a much smaller group where your artistic voice will get much more consideration. This is not fair, but it is the least unfair way to equitably judge 120 applicants for a competition and still retain ones soul at the end.
Also, your compositions will only ever sound as good as the orchestras and ensembles who play them. So consider that, after getting through the 1st round with the calling card of your institution, then you also have the advantage that your recordings will have on them performances by Eastman students, not Central Wisconsin Univeristy-Janesville on it. (With all respect for what I'm sure are some fine musicians at my hopefully made-up university!)
It's a cascade effect.
On geography: I can now say for certain that the coasts are the place to be. There just are more jobs, more artists, more people interested in more new and different kinds of music, more universities, and even if that wasn't true, there definitely are more jobs, schools, and people per square mile! This will be a mega time- and cost-saver to me as I apply for jobs. Anywhere else you go, you can fully expect to take many multiple days off for very simple things like single day interviews and auditions (which I have done). However, just this past week, I benefited from a job interview at one of 5 huge urban areas within a 2 hour travel radius.
As a recovering Texan: while I miss aspects of Texas and certain virtues of my home state, they are far outweighed by all of the virtues enumerated above.
So my top five decision factors would then be:
1. Brand Name Institution
2. Teacher Fame / Teacher Reputation / Teacher Quality / Teqcher Relationship
3. Location
4. Cost
5. Quality of the program
#5 is definitely not the least important, but 1 and 2 almost completely take care of this. At the graduate level, you've already filtered out all of the other hundreds of institutions that wouldn't have "Best" associated with them. Good, Great, but not Best.
Facing facts: the music business is tough. Even with the Peabody Conservatory as my calling card, with the networking and all the rest, finding a job will still be difficult. But every little bit helps. You don't want the job hunt to be a dice throw. You want them to know that they need you. And this is where careful planning and preparation can possibly be worth it in the long run.
