NACAC (National Association for College Admissions Counseling) has a database organized by state. For example, in May 2010, Drew University and College of Mt St Vincent still had openings for qualified applicants. (do a search for Space Availability)
What if you decide in March that you want to apply to more colleges? US News and World Report magazine has a list of colleges that have later than usual deadlines: March 1 or later, often into the summer. Some nearby colleges of interest: Keene State and Plymouth State (NH) have April 1 deadline; Marietta (OH) has a 4/15 deadline. USM takes applications into the summer because some majors do not fill.
links verified 4/2013