Congratulations on choosing Raleigh, you won't be disappointed (perhaps lost on the roads for while, but that will pass).
I took my concealed carry class at the Personal Defense Handgun Safety Center. They have a website at http://www.pdhsc.com
where you can get numbers to call and register for their class. The speaker they had was truly an expert; it was worth the extra money just to hear his stories and inside information about the NC concealed carry laws. I know of other people that offer classes, but none with someone so well versed in law, law enforcement, and concealed carry.
North Carolina is fairly gun-friendly, but with the statutes arranged so that every municipality and business can have their own rules about firearms, it can be a bit overwhelming to figure out where you can and can't carry. You cannot carry in:
-A movie theater
-A state fair
-Any government building, including its parking lot
-Any restaurant that sells beer/wine/liquor
This is because you can't carry in a place that requires an admission fee (ticket) or serves alcohol. Several local malls prohibit concealed firearms, but I'm not for sure that means open carry as well. I would assume yes, until I got it confirmed with a manager.
In wake county, you may have trouble gaining your concealed carry permit, as the sheriff is (from what I gather) deliberately slow in signing off on them. In my county, Harnett (directly south of Wake), I had my concealed carry after a week.
PDHSC is a great, active gun shop with an indoor firing range. I highly recommend them because they are very old-school and are extremely helpful. If you're looking for a particular type of gun range, I'm sure you can find your answers there.