$1,200 in Manhattan is impossbile unless you are looking for roomates and/or don't mind living in traditionally non desriable ares like Harlem or Washington Heights.
Just to give you an idea, a good friend of mine lives in Chelsea in a 400sf studio and pays $2,500 a month.
For $1,200 she's looking at the outer boroughs, Westchester County, Long Island or NJ.
Tell her to check out Craigslist
http://newyork.craigslist.org/