Pros
There are a lot of great students and faculty at Stanford. I believe your experience in graduate school depends strongly on finding the right adviser/research group to match your personality. At Stanford there are a lot of great faculty advisers, but not all of them! You definitely have to take initiative to make sure you get the most out of your experience.
Cons
The university is in a bit of a bubble (it seems students hardly ever go off campus). There is definitely still a fair share of graduate students who are overworked/dissatisfied with their experience (likely because they didn't/couldn't find an adviser that matched their personality. Professors are usually hired for their research, not always their teaching abilities, as a result not all faculty are great teachers.