For someone from out of state, hunting in North Carolina can be pretty challenging - especially eastern NC, which is where Raleigh is located. I speak from experience here, being from WV where there are plenty of places to hunt, the regulations are pretty simple, and the law is consistent state-wide.
Basically, you'll find two primary obstacles. The first is that the regulations are a major pain in the ass to figure out. Each county has a lot of influence on local hunting rules, so what you can hunt for, hunt with, and when and how you can hunt can vary greatly from county to county. With deer for example, some places you have to use a shotgun, some places you can use a rifle, some other places you can use a rifle but only if you're in an elevated stand, that sort of thing. Sometimes just by crossing a river inside a county you can find yourself under a completely different set of rules. Personally, it's difficult for me to relax and enjoy myself in the woods when I'm constantly worried about whether or not I'm breaking some obscure law I've never heard of.
The second big obstacle is simply finding a place to hunt. There is some public hunting land, but it gets very crowded and most of it is a pretty long drive from Raleigh. Unless you know someone who owns a pretty big hunk of farmland (and it's all farmland down here) your only option (and the one most hunters seem to take) is joining a hunting club with land they lease from the owner. That can be a good thing because most of the hunt clubs take good care of the deer herd in their area and you can kill some nice bucks that way, but it can also be frustrating if your style of hunting doesn't match up with the club's preferences. For example, most clubs down here that I've talked to are made up almost entirely of treestand hunters. I'm not big on stands personally, and a lot of the clubs simply don't permit stalking around during hunting hours. Other clubs use dogs to hunt deer, and don't permit treestands, that sort of thing. I guess the key would be finding a club that suited your preferences.
As far as species... varmint hunting isn't going to be very productive down here, I wouldn't think. Squirrels are common, but bobcat, fox and coyote are pretty much non-existent. The black bear population is supposedly growing out on the coast and in the mountains, but I've yet to see sign of one in this area. The deer are plentiful, but much smaller than you're going to find up north.
I guess the point of all of this would be that hunting in the Raleigh-Durham area is pretty lousy. There are some good things about living here, though. The economy is booming. Jobs are plentiful, the payscale is decent by southern standards, and the cost of living is (relatively) low. Drive 3 hours to the east and you've got the Outer Banks and some of the best beaches in North America. Drive 3 hours west and you get into the Blue Ridge mountains and some great hunting, fishing, whitewater, and hiking. Here in the middle though we call it "the home of the hot, the flat, and the ugly."
