Not a whole lot of places to publicly shoot. Here are some links to clubs that host matches and are membership only for day to day shooting.
Ant Hill Range - Southport, NC Hour to hour and a half south of J'ville, but they do have Steel Challenge, USPSA, and IDPA matches (with a 3-gun every month with 5 Sundays) on Sundays. Membership only club, but non-members can get in to shoot matches.
Buccaneer Gun Club - Leland, NC West of Wilmington, 400 yard rifle range, pistol range. Hosts matches but, like Ant Hill, a membership only club (with limited number of slots that can be filled-they have a waiting list).
Coastal Carolina Rifle Club - Stone Bay Rifle Range, Camp Lejeune NRA Highpower Long range and Mid-Range matches only.
North State Shooting Club - Butner, NC NRA Across the Course, Mid-Range, and Long Range. Butner also hosts the Sinclair Fullbore Championships and the Eastern Creedmoor Cup/Games.
As far as public shooting there's
Flatwoods Outfitters - Hubert, NC near Lejeune. Not quite my cup of tea, and can get rather crowded on the weekends, but other than private land, that 's about all you've got. I think there's a range toward Havelock (Cherry Point), but I've not been there. Indoor pistol range in J'ville (Sportsman's Lodge) and Wilmington (Shooter's Choice). Lejeune itself has a skeet range on Mainside between Holcombe Blvd and Piney Green Rd (Sawmill Rd.)
Disclaimer: I'm more geared toward NRA HP with some pistol matches on the side. Some other folks on here probably know a few other ranges that I don't know about.