South Mountains state park has several great backpacking sites. That park is the one closest to Raleigh that seems "remote" in my opinion, though it's about 3.5 hours away. There's hike in camping at the Eno River state park too. It's close, and I really like the park, but the campsite is only about a mile in unless you take an indirect route. Last option I'll mention is Merchant's Millpond state park. It's about 2.5 hours NE. Hike in sites are halfway through a 5 mile loop. It's pretty flat, though it's swampy so I tend to only go there from October - March to avoid heat/humidity/bugs. It's the Northern-most natural habitat for alligators, though I haven't seen one there. (Canoers see them, and you can canoe-in camp. I'm a hiker though so I've missed out on that.) My kids had done all of these by the end of primary school, and I think my daughter (the youngest) had done them all by Kindergarten. Happy trails!
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