How to pick a grad school
A better question is, "How do I pick which faculty I want to work with in grad school"? After you identify them, you then apply to the schools where they teach.
Really, especially for the Ph.D. (and less so for the Master's degree), you will want to pick a scholar or three as possible mentors to work with first, and that will tell you which schools to apply for.
So, talk to your current professors about who are the top dogs in your particular field. Ask in particular if your professor knows any of them personally or professionally, so you can network together to contact them.
Then, spend a weekend at the library going through the databases and seeing what all they've published. Get a feel for how they think and what sort of work they do, and where they teach. Are they doing research in an area that you find particularly fascinating? Look up their C.V.s online or their links on that department's webpage to find out more.
See if you can download a copy of the school's course catalogs online. The school's course catalogs in particular can reveal a lot of hidden information. There's usually a list of the faculty in the back, including how long they have worked at the institution. For the department you are applying, you can quickly assess how many faculty there are and what their ranks are (assistant, associate, full professor, or professor emeritus). A healthy department will have a wide range of ages and ranks. If all the faculty there are fairly new, it may be that the department is refashioning itself after a wave or retirements, or it may be that the department is dysfunctional and there's a lot of turnover. Unhappy professors may be pulling up stakes and leaving, and unstable departments can be a symptom of that.
On the other hand, if the department is composed mostly of people who've been teaching twenty or thirty years, it's currently stable, but a huge wave of retirements might hit at any moment. In that case, you might want to work with superstar scholar X, only to find out that X is very likely to retire at any moment, leaving you stranded.
If it's a healthy department, there should be a wide range of ranks, and there will be both newer and older faculty there, ensuring a more stable rate of change.
Do research on the schools where your professors teach. Find out who else teachers at that department and what they in turn have published. That may help you discover some hidden gems. Once you have a good idea of the department's identity as a whole, you can apply to 3–5 schools.
To give yourself a leg up, in your letters of intent or your application, mention specifically which professors you would like to work with, and mention by title some of their publications. I'd say 90% of applicants fail to do that, and doing that can give you a real leg up on the competition.
Keep in mind, it's the people you want to work with, not just the institution in the abstract. It's the people who give the reputation to the institution, so they are your real target, not the institution for the institution's sake.