Our first installment of unsolicited advice concerned the difficult question of how to get into graduate school; this one presumes that one has successfully leapt the hurdles of GRE's and ornery admissions committees, and is faced with the perilous decision of which offer to accept. (If one has either one or zero offers, presumably the decision-making process is somewhat easier.) We will not, at the moment, be addressing whether you should be going to graduate school in the first place, or how to succeed once you get there. This is a much more difficult task than the first installment. Not that it's more difficult to decide where to go than to get into grad school in the first place; just that it's much more difficult to give sensible advice about how to do it. When it comes to getting into grad schools, everyone agrees on the basic notions: good grades, test scores, letters, research experience. Choosing where to go, in contrast, is a highly personal decision, and what works for one person might be utterly irrelevant to someone else. Rather than being overly prescriptive, then, I thought it might be useful just to chat about some of the issues that come up. Ultimately, you'll have to decide for yourself how to weigh the various factors.
Why do you want to go to grad school in the first place? Sure, maybe you should have already given some thought to this question -- but now is the time to get serious. Is your goal to become a professor or other professional researcher (which is typically assumed)? Or is it just to get a Ph.D., and then see what happens? Or is it simply to learn some science? As a general principle, the purpose of grad school is very different from that of your undergraduate college education. At least in the U.S., college serves multiple purposes: training in some concentration, to be sure, but also a broadly-based liberal education, as well as more general exposure to critical thinking, and crucially important social and personal aspects. Grad school is much more focused: it serves to train you how to be a working research scientist (or whatever, although I'll be speaking as if it is science you'll be studying, as that's what I know best). In college it's good to be a broad person and cast your net widely in the oceans of learning and experience. In grad school, however, there is a lot to be said for focusing as much as you can on the specific discipline in which you are specializing. Not that you should stop having broad interests, but it might make sense to sacrifice some of them temporarily to the goal of becoming an expert researcher. The reason for this is that, like it or not, you are entering a competition. Not necessarily grad school itself (where grading and suchlike are notoriously relaxed, although there may be competition for advisors and fellowships and such), but the ultimate job market. Most people who go to grad school want to get jobs as scientists, probably in academia. There are far fewer such jobs than there are grad students, so most people who get a Ph.D. will ultimately not succeed in becoming professors. And the other people who want those jobs are also very smart and dedicated. So, if you are serious about choosing this as your life's path, it makes sense to really devote yourself to your craft during your grad school years, and give it your best shot. I personally think that the rigorous training provided by a Ph.D. is extremely useful and rewarding even if you don't become a professor, but you should certainly enter the fray with open eyes. If becoming a professor is what you want to do, you should choose your school accordingly. At the same time, I'm a firm believer that your life doesn't completely end just because you're in grad school, nor that the process itself should be unpleasant. It should be extremely challenging, taking you to the limits of what you are capable of doing -- but the days you spend in school are also days that you are alive, and you shouldn't completely shut yourself away. That's the difficult balance to strike. (Told you this wouldn't be very helpful.)
How prestigious is the school and the department? Prestige is something that is much more relevant (to the extent is is relevant at all) to your undergraduate school than your grad school. Not that it's completely irrelevant, but the prestige of your advisor is more relevant than that of your department, which is much more relevant than that of the university as a whole. Of course, there are tight correlations between these different kinds of prestige, but they are not perfect. Although we had a debate about this in comments to the previous advice post, I still think that the identity of the school/department from which you get your Ph.D. is essentially irrelevant to ultimately getting hired as a faculty member. This is not some utopian perspective that we live in a perfect meritocracy in which where you come from doesn't matter; rather, what matters is where you are doing your postdoc(s), not where you went to grad school. Of course, where you do your postdoc might be affected by where you go to grad school! But more important is who your advisor is.
What kind of advisors are available? So now we get to the nitty-gritty. The single most important influence on your graduate career will be who your advisor is. Sometimes you might know precisely who you will be working with before you actually get to the school; this is more common in chemistry and biology than in physics, where the "lab" you will be associated with is all-important. But in physics, it's more common to first arrive at the school, and only once you are there will you try to hook up with some advisor. (I know that MIT accepts people into different research groups, but most schools simply accept you into the department as a whole, without any hard and fast rule about what group you will be in, much less which advisor you will have.) Of course, picking an advisor means picking a specialty. Some people know exactly what they want to do before they arrive; that's not necessary, but it helps. The point is, get some feeling for the faculty members who might realistically become your advisor. Are they active in research? Do they have personalities you could get along with? Do they have sufficient funding? Are they looking for new students, or over-subscribed? Do they let their students freelance, or guide them closely? Do they actively support their students in their later careers, or simply wish them well? Your Ph.D. advisor will very possibly be writing letters about you for decades to come -- choose someone with whom you will be proud to be associated with, and who will take some interest in your well-being. As far as choosing your field of specialty is concerned, many factors come into play. Of course you should do something in which you are interested. But you also want to get a job, and the job market can be different in different fields. (Most notoriously, it's somewhat better in experiment than in theory.) The point is, what specialties represent the intersection of "things you think are interesting" and "things that might lead to a rewarding career"? If that intersection is empty, you might want to rethink this entire process. Keep in mind also that some advisors are harder to get than others. They might simply be more popular, or have less funding, or about to switch fields or go on a three-year sabbatical. Find out! There is no rule that says that, simply because you've been accepted to a department, the faculty member of your choice must take you on as a student. All else being equal, it's nice to maximize the number of faculty that you might possibly wind up with as an advisor. Much can happen along the way to your Ph.D., and it's good to have options.
What is the scientific environment like? Grad school is a crucially important time of your life, when you make the transition from being a student to being a researcher. You won't do it alone. Are the other students in your prospective department and group people who you could learn things from? What about the postdocs? Postdocs, who are experts in their fields but were just recently students like yourself, are often the most valuable sources of insight as you are struggling to learn the ropes. What about other professors in the department -- could you imagine dropping into their offices to talk about science, or are they overly intimidating (or, much more likely, never around)? Do people have lunch together, and hang out more generally, or does everyone go their own way? A supportive and useful environment goes a long way to molding you as an effective researcher in your own right.
What are the departmental requirements? A couple of years ago the University of Chicago held a celebration for the centennial birthday of Enrico Fermi, who was a Chicago faculty member. The department brought back a number of people who were graduate students in the 1950's when Fermi was there. Put them all in a room fifty years later, and do you know what they talked about? The candidacy exam, that hazing ritual by which a young student proves that they are ready to take on research. Different departments put up different [strike]hurdles[/strike] requirements between you and your Ph.D. What are the required classes? Are there many breadth requirements? Are the courses interesting, and are the faculty good teachers? Is there a general exam? An experimental requirement? How long does it take to get a Ph.D.? (This last question is likely to vary significantly from advisor to advisor -- some advisors like to keep their students as worker bees in their vast empires, while others consider students a burden and want to get rid of them as soon as possible.)
How is life as a student? Probably the single most useful way to learn about different schools is to talk to the students who are already there. Email them, or seek them out during visits. They will usually be willing to give you the inside scoop (and will be much more well-informed and honest than faculty members). Is there competition for the best advisors? What is the departmental atmosphere like? Do you get nice offices? The more students you can talk to, the better -- people can have wildly different experiences in exactly the same environment, so it's good to collect a bunch of data. "Life as a student" includes life outside the lab. What is like to live in the location of this particular university? Is it a big city or a college town? (And which do you prefer?) What is the cost of living? Are there dorms, or do students generally live in apartments? Do you need a car? Details, details. Are the necessities of grad student life -- movies, coffee, pizza -- within easy reach?
How would you be supported? Another crucial issue. At some point you may have had the happy realization that most grad students in the natural sciences don't actually pay those exorbitant tuition bills -- in fact, you typically get paid to be a grad student, either through teaching assistantships, research assistantships, or fellowships (in roughly ascending order of desirability). So, is there enough support to go around? Is the stipend enough to actually live on? What are the chances of getting RA's or fellowships, so that you don't have to teach all the time? Getting some teaching experience is extremely valuable and rewarding, and you shouldn't avoid it entirely. But it's not the reason you are in grad school. Research is hard, and takes a lot of time -- if you have to teach a huge amount, it can slow down your progress towards a thesis.
What should you do about your significant other? Now we're getting serious. So you want to go to MIT, but your sweetie has the job of his/her dreams in Seattle. Should you suck it up and accept the offer from UW, or try to make a long-distance relationship work? Or forgo the temptations of romance, since your career is more important and love never lasts anyway? Look, I can't help you here. All I can do is sympathize and recognize that these are real issues, not trivia. Like I said, your years in grad school are years of your lives, and shouldn't be sacrificed utterly to your work. But sometimes a long-term plan involves temporary steps backwards to achieve a better ultimate goal. You have to decide for yourself, keeping in mind that there are no objectively right answers.
That last little motto applies not only to romantic entanglements, but to choosing a grad school more generally. It's really hard to know ahead of time what place will be right for you. Different people will have very different ideas from mine, and you should listen to all sorts of perspectives (which will hopefully emerge in the comments). Think about it carefully, but don't be afraid to trust your instincts as well. Your comfort level is important. If, after making your decision, you feel as if a great burden has been lifted and you're happy inside, you've probably done the right thing. Good luck!