> > I will be making the big transatlantic trip to the States in late July, with my parents.

Remember to stay on the right side of the road.
When you get on Interstate 81 in Virginia, you might want to continue south to Knoxville, Tennessee and the Great Smoky Mountains National Park. That would put you in the area of Dollywood and would line you up to visit Nashville and Memphis along I-40. So many people from across the pond come to the U.S. and miss the south (The best part!) Myrtle Beach, South Carolina has the best beaches in the world. Florida in beautiful, especially the Keys, and Atlanta will blow your mind. It would be a shame to miss New Orleans with all the good food, history and sleazy chic of the French Quarter.
Texas is one of a kind, and moving west, New Mexico is breath-taking and empty. Don't miss Las Vegas, and then suddenly you are in California. The United States doesn't stop there, but if you are driving, that's far enough.
My guess is that wherever you go, it will be a great trip. Having crossed this country a few times myself, I think you will find that it is bigger than expected. It still blows my mind.
Howard