Sometimes people ask, why did you pick CMU? In order, it was 1. students, 2. profs, 3. outcomes, 4. everything else was fine. I think that decision order is pretty ok, but maybe profs should be tied for #1, not sure.
But! In more detail:
1. Students: I just felt pretty well at home with the students here. Hard to say why. Ok, not much more detail here, other than to say: this is important! Both the existing students, and the other incoming ones, will be working with you for many years. Maybe hanging out outside school too, depending on the place. (we're pretty social at CMU). You'll probably spend more time with them than the professors. You get a half a minute to get to know them at open houses, so that's frustrating, but if you find you really like (or dislike) the students at one place in particular, take that into account.
2. Professors: best case, you find an advisor. Second best case, you find a group of potential advisors where you'd be happy to be advised by any of them. (more info on this decision) If you don't have either of those, don't go to that place. Your advisor relationship is suuuuper important. More important than a typical boss. They will not only be your boss (so they can make your life easy or hard) but they will also be some inspiration, introduce you to other people, etc. So make sure you have an advisor idea before you sign the form.
One side note: if one place has your #1 top choice advisor, and another place has your #2 choice, go with #1, obviously. But if one place has your #1 top choice, and the other place has #2, #3, and #4, and you've never worked directly with any of them before, I'd say go with the 2-3-4 place. There's a lot of randomness that you don't figure out until you work with someone, and someone who seems perfect might just for whatever reason end up not a perfect match. So in that second case, go with the #2 advisor, and you've always got 3 and 4 if 2 doesn't work out.
3. Outcomes: notice what the graduating students are doing. If they're all getting the kind of sweet jobs you want to do, that's a good sign. If half are doing startups, and you want to do a startup, great! If they're all going to industry jobs, and you want to be a prof, not so great. If 2/3 of them are dropping out and sitting at home wallowing in depression, probably not so great either.
4. Everything else: these will probably not factor into your decision, but look out in case they do. City, stipend, classes, quals, teaching, office space, etc. Usually these will all be fine: the city is ok, the stipend is about the same, you have to take ~8-10 classes, you have to pass through some hazing ritual such as quals or comm talks or extra classes, you have to teach 2 classes, your office is a desk in some depressing basement, etc. These are all fine. But this is an area where there can be red flags: if you don't have a guaranteed stipend, if you have to teach every semester, if the city is super expensive and difficult to live in (lookin at you, Stanford) or in the middle of nowhere and depressing to you, the hazing/quals makes half the students quit, etc. If there are any red flags, they should factor into your decision as much as the above 3 points. Otherwise, don't worry about these things, they're fine.
So! If you've considered all these, go with your gut then, and you'll do fine. Also, if any current prospective students end up reading this and want to talk more, find my email (or twitter), drop me a line.