Re: the two housing questions above, people live all over. School does not have any sponsored or subsidized housing - sometimes there is a spreadsheet to find roommates and/or link up with upperclassmen who are moving. Around this time of year upperclassmen start advertising listings for their place on class Facebook groups as well. Other than that, utilize StreetEasy or other websites, and be SURE to check of that you want a No Fee listing - Realtors fees can be a killer.
If you're going to live outside of Manhattan, take into account commute time and cost when considering how expensive or not something is. A lot of areas in Brooklyn and Queens are WAY more expensive than Harlem or the Bronx. Some students drive or take the train from Long Island or NJ, and some take the subway or bus here in the city.
I can speak for my class in that we have a decent chunk of people who live in Harlem, a lot of people within Manhattan, and still a chunk who come from Queens, NJ, or LI.
As far as rotations, it depends on where you land. Some rotation placements involve multiple adjunct sites, so having a central location and a car would be ideal in that case. Some rotation placements have everything in one spot, so living close would behoove you instead. A lot of the NJ gang who commuted originally are just staying where they are. Long Island commuters who got lucky with their placement will also be staying put. Some folks are moving elsewhere in Manhattan, or down to Staten Island or Brooklyn. Obviously the folks who are out at Southampton or deeper in Jersey will have to move out that way.