Pros
Overall, Stanford is an amazing place to work. The environment and benefits can't be beat. You can go for a swim on your lunch break or a walk around the lake. The recreational classes and opportunities are usually great. Eating at the dining hall, although pricy, is a real treat.
Cons
If you're not senior management, faculty, development, etc., Stanford's pay has not kept up with the cost of living in the area. If you come for a job from outside of California, be prepared for a real shock when you see the kinds of rentals and the prices. Beauty has a price. You will not be able to live near campus as the average employee. Unless you're really familiar with the traffic in California, don't look at places that you think are an hour away, because they'll be two hours away by car. And you'll have to pay to park on campus, so not driving at all is your best option.
Many administrative jobs are held by partners of people working in tech or faculty, because that's the only way you can afford to live there. If you don't have a partner making $200K+, you'll be taking the train or bus for an hour. If you're thinking about buying a house and you don't have a suitcase of cash, that sound you're hearing is my laughter.
It's also important to realize that the working conditions across campus vary by unit. Working at the Graduate School of Business will seem more like a corporate job; working in Medicine could be brutal; and the treatment you will get can vary by department.