We've rented beach houses on Sunset and Ocean Isle Beach. They are both nice, but we prefer Ocean Isle. It's kind of quiet, not much to do on the island but a small museum, mini golf and restaurants, but it is a great place for families. The water is usually really warm by mid June too!
By the way, Ocean Isle Beach is in the southern part of North Carolina. It is about a 40 minute drive from Myrtle Beach, and about the same amount from Wilmington which has some fun stuff to do as well. We also sometimes take a day trip to Charleston, SC.