Pros
The location cannot be beat. Northern California is a place that people move to and do not leave for the rest of their lives. Graduate students here are generally very well funded, especially compared to other universities. As a private institution, Stanford is not as susceptible to the whims of budget and funding problems. There is a certain air of pride in the air that whatever Stanford does, it does well. The school of education, where I work, is very good compared to the most of the top ed schools, especially when it comes to funding and support. Facilities are comparatively good.
Cons
Palo Alto itself is a terrible place to live and work. Obviously each graduate field has its own micro-climate within the university. The on-campus food is beyond terrible. There are no good options other than Jamba Juice. Can't live on that for too long.