I'm not sure what will be in bloom at that time of year, but some places that come to mind are:

North Carolina State University's Arboretum in Raleigh.
http://www.ncsu.edu/jcraulstonarboretum/index.php

Pullen Park may be worth a look.
http://www.raleighnc.gov/arts/content/PRecRecreation/Articles/PullenPark.html

The Elizabethan Gardens in Manteo.
http://elizabethangardens.org/

The botanical gardens at Duke in Durham, NC are gorgeous too. There's a botanical garden in Fayetteville (about an hour from Raleigh) but I've never been there, just driven past.

If you're up for a longer drive (3 hours or so), I love the botanical garden in Norfolk, VA. For a 4 hour trip from Raleigh, there's Biltmore in Asheville, NC. I'm not sure what'll be in bloom in February in the mountains, but whatever it is, I'm sure Biltmore will have it and it'll look gorgeous.

Duke: http://www.hr.duke.edu/dukegardens/

Fayetteville: http://www.capefearbg.org/

Norfolk, VA: http://norfolkbotanicalgarden.org/

I'll second the recommendation for the Arboretum. It's not a massive garden, but there's still plenty to see.