I am planning to live in graduate housing during my first year, so that I get to know the good places and potential apartment-mates before I actually rent an apartment. I did the same thing during my undergrad: lived in the dorms during freshman year, and then rented a 3-room apartment with two other students. Incidentally, Brown seems to have a graduate housing program for just that.
From what I have seen so far, graduate housing need not be like undergrad dorms though there are certainly a few of those too. Several universities (like Stanford) seemed to have a lot of apartment-style housing for grad students and also some studios and singles.
I am wondering if it would be worth paying the extra money for a single...for the privacy, you know (see the last line of Will's comment
). By the way, even dorm-style 1-person room graduate housing would give us more privacy than living in an apartment, would it not?