Pros
I was a graduate intern at Emory for two years. I worked with a great team and had the opportunity to interact with faculty and staff throughout the campus. Most of the people I had the opportunity to work with were lovely and made the job really pleasant. I felt like I was given increasing responsibility and really enjoyed the level of trust and freedom I received from my supervisors, who are some of the most passionate and energized people I know.
Cons
The most difficult part of my experience was interacting with the student body (a requirement for some of my work duties). To make a sweeping generalization, I found them to generally be egocentric and largely apathetic, probably suffering from rich private school syndrome. I have worked with public universities and have never had the same experience. Something to consider if you will be working directly with students full-time.