We keep our boat on the New River in one of the two marinas on board Camp Lejeune and have been there on and off for six years. There is good sailing in the upper part of the New River, above the Snead's Ferry bridge. Below the bridge the river is shallow except for the channel. We usually sail in the wide part of the river off the New River Air Station - good depths and winds. Most days we end up anchored in one of the creeks along with another boat or two. There's an on-again off-again sailing club at Lejeune - the Ragged Point Yacht Club - that hosts monthly races when there's enough interest.
Camp Lejeune will shut down the waterway when certain ranges are hot. There usually aren't any restrictions on New River itself and when training is going on in the river it's easy to avoid.
We motorsail in the waterway frequently. Wouldn't recommend sailing in it due to traffic and narrowness.
The weather at the end of June is usually good for sailing - the sticky heat isn't on full time yet and the daily afternoon thunderstorms don't show up until later in the summer.
I know two guys who've sailed out of New River Inlet. One only drew 3' and went during an abnormally high tide; the other lost his mast and keel when he went aground and got rolled.
We've made the run from New River to the Chesapeake four times; you'd be hard pressed to make it in less than five days.
If you make it down here stop by Gottschalk and look us up.