Welcome aboard!
I live in Charlotte, and travel occasionally to Raleigh on business.
Whenever possible, I stop in the Uwharrie National Forest and shoot. It's about an hour and a half from Raleigh.
Take the Outer Beltline to US-1, follow US-1 to 64 west. Stay on 64 westbound until you get to hiway 109. Take NC 109 South about 9 miles to the third "Badin Lake Recreational Area" sign (or something similar, it's the third "park" sign), and turn right (you can't turn left). About 200 yards down, you will turn right again (marked) and follow that dirt road about, oh, I guess about 4 miles, and an unsupervised covered 8 or ten lane 100 yard range will be on your left. It's called something like the "Eagle's Nest Range" or "Thunderbird Range" or something from a Boy Scout manual.
Anyway, there may be one closer to you, but that's the only one I know.
Oh yeah, you'll pass a gas station on your right before you get to the turn off 109.
I believe these directions are correct. If not, the locals at the gas station can help.
Happy Shootin'!