I live near you it seems
To Wilmington/Wrightsville from here it is 1 hr 50 mins if you are a fast driver
When my oldest child was young, I used to take her to White Lake. There is a public beach area. It's a clear lake, always clean, fairly shallow, and you can let your kids play in the water without worrying about waves. My young daughter used to sit in it and play and I could actually sit on the sand and watch her. At the beach I always stayed in the water with her. It's on the way to Wilmington..if you don't use I-40. Sorry, it's been yrs since I went, I don't recall how to get there or its exact location. I do know that it's been talked about on CD many times so you could do a search for it.