I know a few folks that have children such as yours in Wilmington, most of them younger than high school age.
Some of them are in the public school system, some of them are in private schools. I would say this about Wilmington...its public schools have the ability to handle these children, but there are also a number of good private schools that can also handle them.
One of the things about Wilmington is that it really does have it all, the same quality stuff you would find in Charlotte or Raleigh, but its just a smaller place, on the ocean.
I also have an extended family member that does not live in Wilmington and comes there every year to participate in this....
Surfers Healing
with their child, they swear by it and many folks around town really believe in the ocean's benefits for these kids. I don't think you should have any doubts about Wilmington in this regard.