X2 Savannah and X2 Charleston - Charleston park with lights, James Island County Park has a very liberal cancellation policy, can cancel one day before and get refund so ask to go on the waiting list. I have done this many times and usually get in. Too bad so many people reserve and then decide later, makes it hard. It is worth a visit, there is a KOA a little north of the city on Hwy 17, so can stay there and visit Charleston and just ride through park to see lights. Beautiful city, fun at holidays too. Savannah ditto, no parks close to town, but nice one just west of I95 and another we stayed at out near beaches. Either will require ride to city to see sights, same a Charleston but I know JICP has shuttle, not sure about ones near Savannah. Consider Jekyl Island? Nice park on Island, but go if you just want to camp, not a whole lot to do there. Park is heavily wooded and near north end of island.
How about east coast of Florida, lots of parks in the St Augustine, Palm Coast, Fernandina Beach area and several are ocean front or sound front and ocean access. Lots to see in St Augustine area.
Go a little further north and lots of opportunities in Myrtle Beach SC, I would highly recommend Myrtle Beach Travel Park, nice place lots to do in area and very kid friendly, if that is concern.