My first advice would be to expect ANY kind of weather. When my daughter graduated from Barnard back in 2009 we were SO COLD during the Barnard ceremony on campus and then were SO HOT two days later for the University-wide ceremony…and we all got sunburned!
The official graduation with all the students (the one on May 20th this year) will be LONG and rather boring, but don’t miss it! You will need to get there early to get seats and it will be crazy crowded. After various people you probably won’t know are recognized and awarded honorarial degrees, each school group will be asked to stand and their respective deans will step up to the podium and ask the Columbia University president to confer the appropriate degree upon them. This will include Columbia College, SEAS, Barnard, the medical school, school of Social Work, Teacher’s College, etc.
I do NOT think there were concessions… maybe bottled water was available?
The smaller individual school ceremonies are where the students actually “walk” and get to shake hands with the dean and such. There are interesting speakers (my daughter’s was Hillary Clinton) and it’s more personalized than the huge University ceremony.
You can find out about other commencement week activities here: http://www.columbia.edu/content/commencement-week.html