Good call Dingo! Coffeehouse is wonderful and one of the highlights of every month! If you want to get a sense of the culture at P&S (and have a blast while doing so!), I would strongly encourage you to try to attend.
It's a good question. Admittedly, I live in Bard Hall, so my perspective might not be what you're looking for, but here are my two cents anyway. You're right that the majority of first-year students do live in Bard Hall, but many live elsewhere for any number of reasons. As far as I can tell, they are as engaged with student life here as anyone. Bard is great as a centralized location for organizing our community, but it's always open to everyone in the class. Also, we spend so much time interacting with each other outside of living accommodations (in lectures, in clubs, in clinics, in small groups, in the library, in the gym, etc.) that it's virtually impossible not to know everybody and be a part of things.
You're also right in that many people opt to stay nearby, but a chunk of students live 50+ blocks away and they seem to enjoy broadening their NYC experiences. The A train makes all of the west side pretty feasible for living. I think that the farther away you live, the more proactive you might have to be. But the bottom line is that, in my experience, the community here is extraordinarily inclusive and welcoming to everyone. If you want to be involved (no matter where you live or, even, what you're interested in), you will be. Come to Coffeehouse to see what I'm talking about!
Hope that somewhat addressed your question and my apologies for rambling!