Public transportation in Raleigh will get you to most places, though it is stil somewhat limited. The great news for students is that, with a Student ID card from a University in Raleigh, you can ride the Capital Area Transit (CAT) and Triangle Transit Authority (TTA) buses for free!
A great site about the transit systems in the area is GoTriangle.org, where you can enter your start and destination addresses, along with either a time to leave or a time to arrive, and it will give you possible routes which include CAT, TTA, and walking, to help you reach your destination. It's a great site for getting around the area!
Other sites that you may find informative: