Codoras State park is east of Gettysburg, (south/east of Hanover, 40 minute ride), nice park but the pool won't be open that early. There is also Caledonia State park to the north/west, near Mt. Union(20 minute ride), and Pine Grove Furnace State park(35 minute ride) almost due north of Gettysburg. The advantage of the state park (at least here in PA) is that at a private campground, the security guy is usually a retiree, with no real authority, but at the state park, the park rangers have the power to arrest, so unruly patrons are dealt with differently.

On the negative side (for some), state parks do not allow alcohol

, but they will not search your bags when you enter, so as long as you are discreet, you'll be fine.
Rt 233 connecting Caledonia park and Pine Grove Furnace is a nice section of good pavement. Not "twisty", but curvy and fun.