We loved Chippokes Plantation State Park. They have new section with water and electric hookups and new bath houses. It's about A 5 minute drive to the free ferry which drops you right at Jamestown. It runs every 20 minutes.
Chippokes is an awesome campground as long as you are in the newer loop. There is even a huge pool. We haven't been there in a few years, but at that time there was NOTHING else on that side of the river. No restaurants, no shopping, no nothing.
Also done the city CG a little north of Newport News a couple times. Nice CG. Convenient to what is north & south of it. Great maritime museum nearby with a full sized replica of a Civil War gunboat & enough to keep a boater interested for most of a day.
Boat: 32' 1996 Albin 32+2, single Cummins 315hp 40+ night per year overnighter
We enjoyed staying at the Newport News Campground. It is some kind of city or country park--heavily wooded with a small lake. It is centrally located to Yorktown and Jamestown.
I would go back there for any future visits to the historic triangle of Jamestown, Yorktown, and Williamsburg.