Welcome to NC. I moved to NC in '94 from NY. Live about an hour west of Charlotte. Enough deer around the house where they are becoming pests. Sprayed 'deer repellent' (smells like stale horse urine) on the flowers and plants in front of the house yesterday - deer think we have a salad bar. Just starting to see this year's crop of fawns.
As far as hunting, technically legal to hunt with firearms around the house, but limit myself to string and stick options. Over past 20 plus seasons have hunted locally on both private and leased property in NC and SC. Currently have access to some small plots of private land, but with the liberal limits, see few decent sized animals. Also on a 1600 acre lease up in the mountains. Fewer deer, but with persistence and patience, one can find some nice trophys on the property. So called 'musket' season comes in during middle of archery season. Pretty popoular, at least locally.
Would suggest you visit local gun clubs and gun shops and inquire about lease openings. Most clubs around here are filled by now, but usually have waiting lists if any good. Occasionally someone drops out late creating openings. Private property can be tough. Being 'not from around here' makes it difficult. Many properties have been hunted by the same group of friends and family for years. You will need time to work your way in. I was lucky when I first moved to NC. Got invited almost immediately by some hunters at work to join them - for 'musket' season. Was told by others at work that they were never invited when they move here.....
Hunting opportunites are available, just may take a little time to find them.