Hi Orims,
Absolutely! There are a number of cultural and international student associations here at Stanford, and I am sure at any other university as well. The bigger the school, the more the population of international students and more likely it is for international organizations to be active. At Stanford, there is a huge Chinese association as well as Indian association. I know they have regular events and cultural celebrations. There is a big mentor-mentee program in the Indian association at Stanford, where you can get help and advice on pretty much anything you want to know about. Besides these formal organizations, no mater what your nationality may be, I can guarantee that you will find a number of students of similar interests and backgrounds that you will like to socialize with.
Besides your own culture, there is a lot to learn about other cultures. At Stanford in particular, there is never a dearth of different and interesting things to do. There are a number of international (South American, European etc) dance events and lessons all year round. I went to Georgia Tech for my undergrad, and the story was no different there either.
In summary, I feel the "big" schools you are referring to will only have these activities and programs compounded!
Good Luck!
