March makes it tough
First off, probably too late to get back to Disney fills quickly during school breaks, I alway make reservations there either about a year early or within 30-60 days of arrival, lots of cancelations that close.
Now, March means likely you will want to go south or near coast. One option is Myrtle Beach, SC. We stay at Myrtle Beach Travel Park, ocean front camping but has wooded section too. Lots to do at the cg and nearby. They have indoor and outdoor pools, lazy river, game pavilion and beach. Out door theater with entertainment on weekends some times of year. LOTS of stuff to do near by if you are looking for "touristy" stuff. They are easy to find on line.
Jekyll Island, nice heavily wooded campground on north end of island, not a lot to do there but lovely beachs and great bike riding and hiking opportunities.
Other possibilities near coast are Charleston SC, wonderful campground at James Island County Park, has many miles of trails, river fishsing access, and playgrounds. There is a water park there but I think closed in march. There is something there you don't see at many campgrounds, a climbing wall. Simulates rock climbing in a very controlled, safe environment. You are about 5-10 mins from down town Charleston and all it has to offer. Not far off are plantations and other attractions. (Air craft carrier, aquarium, historical fort, beaches, etc...)
Georgia coast has some beautiful camgrounds too, just not lots to do for kids. Hilton Head Island is nice, campground/marina near bridge is nice stay (not woodsy though). Nice place to visit, can go to Dafuskie island by boat from there, very interesting - can rent golf cart to go around island and visit virtually isolated beaches and such.
Let me know if you want more info - we camp lots around the southeast. Best bet for young'ins is probably Myrtle Beach.