Sorry if you already know this stuff/it's not clear enough/it's already been said/this is too late.
The towers on South U are quite expensive and in general I've heard they're not kept up well (I've had 2-3 friends try them out as undergraduates). Is 1000 after rent and utilities? If not, there are lots of much cheaper options that are still fairly close. I live in the Elbel neighborhood on south-ish campus, just north of the stadium if you want to find it on a map. It takes me roughly fifteen minutes, at the very most, to walk to the school of social work (which is quite nice, I think). It's mostly undergrads, but our specific area (closer to Main than State) doesn't get too loud. It's mostly just east of State St. and south of South U that might get a bit loud (greek life is around there).
That being said, many graduate students prefer the Kerrytown area, as well as the neighborhood east of it (Katherine/Ann area, can't remember what it's called). Both are short walks to central campus (same distance from my place), are more affordable than the large apartment buildings right on campus, and are much, much quieter. They are also virtually downtown, so you would have some nice options for food, coffee shops, book shopping, record shopping, or whatever you like. West of Kerrytown is the Old West Side which might be less walkable. There's a parking structure near the SW building that I think allows for blue permits (whatever that means), you may want to ask someone at your school if that would be a viable option.
You may wanna check the bus routes. There are blue buses, which only traverse the length of campus and white buses which go off campus and out of town. They are both free to students, but white buses run less often and on a tighter schedule. Blue buses typically run every ten to twenty minutes. I live about two blocks from a blue bus stop, and I find it very, very convenient. There's a stop on the commuter south on South U right next to the SW building, so you could in theory just jump on it and ride it home (if you live south of campus) without worrying about the cold at all.
Finally, because you live in Lansing, I would highly recommend you tour places before you commit. You'll probably be looking at houses that have been subdivided into smaller units. Sometimes they do this in very weird, inconvenient ways. Because the school is so big, there's a huge influx of students coming in all the time, and the developers often build at breakneck paces to have things finished by the day before school starts. Don't commit to something that hasn't been finished yet.
Anyway, hope something in that helped.