The last time I was there I played at a little place in Kitty Hawk but I've just done a google search and it doesn't appear anywhere. Not sure what that means!
I know that Longboards Grill out on the highway in Kitty Hawk has a side room with tables. I can't remember if they're 8 or 9 ft, but they were having pool tournaments at one time and are open all year. The Fraternal Order of Eagles building there on the sound side also has tables and a bar but I've never been.
P.S. Longboards FB wall shows current weekly tournaments.