I recently moved to the eastern part of North Carolina, and am wanting to get involved in some form of competition shooting (IPSC, IDPA, 3 gun etc.)  Can anyone point me towards some matches reasonably close to the Morehead City area?

There's quite a few matches that take place within driving distance from Morehead.

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We periodically host Action Pistol Jackpot matches in Pamlico County. SAFEshooters

B&Rs gun range in Havelock has matches a couple times a month.  USPSA and CQB rifle stuff.

Based upon your question, Highpower Rifle may not quite be what you're looking for, but here it is anyway.

http://www.coastalcarolinarifleclub.com

Mid-range 600 yard and Long Range 1000 yard matches at Camp Lejeune's Stone Bay Rifle Range.


http://www.northstateshootingclub.com

Across the Course  (200/300/600 yard), Fullbore, Mid-range, Palma, and Long Range.



Little bit of a drive, but Ant Hill Range near Southport holds Steel Challenge, IDPA, USPSA, and 3-Gun.  Depends on which Sunday of the month.

Buccaneer Gun Club near Wilmington hosts much of the same as Ant Hill.