Pros
Stanford is a very rewarding place to work as a postdoctoral scholar because you are surrounded by many very bright and sometimes enthusiastic colleagues. Stanford has amazing resources available in terms of equipment and expertise, so you should never be limited in what you would like to pursue by have lack of access. Stanford's School of Medicine Career Center is very helpful and sponsors many interesting career-related forums, career fairs with local employers, etc..., thus providing many opportunities to learn about opportunities and to network. The main University career center is also quite useful and offers 15 minute same day or 45 minute scheduled career advising sessions.
Cons
Little opportunity to stay on as a Stanford employee following postdoctoral training.