You do not need to be a member yourself, but you need a member to sponsor you. Alumni, faculty, graduate students and associate members (anyone who wants to pay to join) can all help you out. The building is quite lovely. I should know, I worked 2-3 weddings every weekend when I was a student there long ago.
Another spot on campus is Dabney Gardens. It is the courtyard for one of the liberal arts buildings, and it is also a lovely spot, and I am pretty sure you can use your own caterer. I don't know how to book it, but I image you could contact the Institute and sort it out in a call or two.