Check out Chippokes Plantation - it's a state campground on the south side of the James river - about 30 miles from Williamsburg. There's a free ferry to Jamestown. You could take a 25 Airstream on it I think, but don't go during the busy hours, it is a commuter ferry. It's amazingly rural compared to the north side of the river. I'm not sure whether it opens in March or April, but it's only about $25 per night, and you can tour the plantation buildings, fields, birds, etc.
GT1963 and I recently camped out at American Heritage RV Park. It's one of the few open year round - and it isn't a huge KOA monster either. Quite nice and very convenient to Williamsburg. Pricier... but that's a tourist area. Got Good Sam?
Busch Gardens and Water Country USA will probably open for the weekends as soon as the weather breaks. Kids love it, (I puke). The historical area is fascinating but tiring on the legs - stop, eat and siesta. Take two or more days and you'll enjoy more. Richmond is less than 2 hours west and if you want to study the Confederacy, you'll find it pretty well preserved. (Believe it or not, Arthur Ashe's statue being put up on the Avenue of the Confederates was rather a bigger deal than it should have been.... and this 20 years after we had a black governor!).
Norfolk/Virginia Beach is about 2 hours east. Can you say NAVY? There are several museums and you can even tour a WWII Battleship in downtown Norfolk. A harbor tour is worth the money IMHO. In Newport News the Mariner's museum is really interesting - and they recently brought up the propeller from the Virginia (see battle of the Monitor & Merrimac). Fort Eustis is an army base with a transportation museum.
Call the state chamber of commerce - they will send you WADS of information on whatever interests you most.
Today is a gift, that's why they call it the present.