Craigslist is probably going to be the most current for listings - you might look at the Raleigh Chamber of Commerce website - or Google for a "Moving to Raleigh" or "Visiting Raleigh" website - for contacts for leasing/renting.
Cary is way expensive & yuppified.
South Raleigh, and cities to the south are more "southern" in tone. But they also contain 'problem areas' - concentrations of low/un-employment housing, etc.
Raleigh strives to be cosmopolitan and has tried to throw off the "redneck" aura of being a southern city.
West of Raleigh along US 70 (west of Crabtree Valley Mall) has a lot of apt. complexes - between Raleigh & Durham.
Western Boulevard (borders NCSU) has a broad spectrum of apts. - mostly for students, but also for employees - the further away from campus, the lower the rents.
[Disclaimer - I lived in Raleigh briefly almost 20 years ago - so my info may not be completely current].
I'll keep on trying to remember other areas for you to check out. You'll find a sort of economic continuum in the rental housing market: student housing, grad student housing, RTP employees.
http://www.zillow.com/raleigh-nc/rent/