In general, NC is an excellent place for cyclists of all persuasions.
Durham is centrally located and a convenient home base for cycling trips all over the state.
Also, don't let stereotypes of Durham's crime rate dissuade you. The small percentage of bad neighborhoods unfairly taint the reputation of what I consider a very nice place to live. Click the first icon in my sig for some snapshots and web links.

This part of the state is not very hilly, granted... but isn't exactly flat either.
Here are some elevations of two of my favorite local rides as an example: