The big ones are NC State here in Raleigh, UNC in Chapel Hill, and Duke in Durham.
There are also several smaller schools such as William Peace University, Meredith College, St. Augustine University, as well as Wake Technical Community College. Durham also has North Carolina Central University; a traditionally African American educational institution.
All in all, there are about 29 colleges or universities within a 50 mile radius of Raleigh.
If you are planning on attending a public university, you might want to know that North Carolina has a one year residency in order to qualify for in-state tuition.
Hope that this helps!