Grad students are a serious lot here. The partying, councils, and extra-curricular activies are focused mainly on the undergrads.
The "one big family" feeling here isn't pushed because the school is rather small. The closeness that does happen comes naturally because we students see so much of each other. It helps that there are lots of mature students too. I get to know people in the computer labs. Everyone is having difficulty downloading, remembering passwords, etc. We commiserate!
Stay with what you are comfortable with. I have volunteered to be a student advisor, but I'm not working and am in class only 2 days a week. No, I'm not going to all the "meet and drinks," but I will go to a small wine & cheese do so we can meet the faculty and more of our cohort.
I have only a year here, and my priority is doing well with my degree. As for partying, we'll have our memories!