We love visiting the US and travel there frequently. Just a few ideas for you to consider:
1) the Smithsonian is huge, it is many different free museums, you could easily spend a week there just visiting museums if you have the time.
2) If you are at Norfolk, Virginia Beach is one of the nicest beach towns around, not too rowdy and more civilized than places like Myrtle Beach or Daytona Beach.
3) Asheville is a really nice town to shop and eat, spend some time downtown. Also the drive on the Blue Ridge Parkway is amazing, try to fit it in, even if it only for 10-20km.
4) there is a really nice drive from New Orleans to Florida via Mobile Alabama along the coast. I do not recall the name, but I remember that it does involve a ferry trip near Mobile.
Also for picking places to stay for the night, we really like KOA for urban stops, they usually have lots of things to do at the campground like swimming pool and often have shuttles into the city they are nearby (like the one in New Orleans). National Parks and State parks are quite nice and very natural, they offer more privacy and usually have something natural to see in the park (a waterfall, mountain, cave...).
Enjoy
