in NC - which you asked specifically - as another poster mentioned, Outer Banks/NagsHead area has great beaches, and also is location of Kitty Hawk (Wright Brothers), so some historical stuff. Also, that are is general location of "Lost Colony" (in addition to Plymouth, MA, another group of British people came to NC area and basically "vanished") - historically there has been a neat outdoor play about their history.
in Va - there is historical Williamsburg, which is a "recreated" colonial-era town with blacksmith, etc., and there is also a Busch Gardens amusement park there. As a kid, starting when I was 5 or 6 (I was the youngest), our family drove to Williamsburg from Ohio at least 4 or 5 times, and always enjoyed it. There is also Virginia Beach - a bit less "glamorous" than in past, but still quite nice. There is also Monticello (Thomas Jefferson estate) and Mount Vernon (Washington estate).
One quick warning about Baltimore - although the "inner harbor" area is nice (which is location of aquarium), be forewarned if you attend during any sort of holiday weekend, etc. The aquarium will likely be so crowded that you will literally be lucky to view one or two exhibits of the entire aquarium - most of the time you will be packed four or five deep in wall-to-wall people of essentially "bumper-to-bumper" pedestrian traffic as you trudge through the aquarium, and at best will see the fish, etc. that might be swimming near the very top edge of a window that you peer as you look over the four-or-five deep rows of people.
NJ- this may sound odd for a family, but Atlantic City can be a great family vacation. We will often go for a four-day stay or so. If you stay right on the Boardwalk (where the "action" is), particularly during the week (weekends sometimes a bit more expensive, but less so since the recession), there are GREAT BEACHES right there, and lots of activities, and surprisingly many families, particularly as you head for the mid/southern Boardwalk casino-hotels (Ballys/Caesars/Trump Plaza/Tropicana). One of the piers is a mini-amusement park with a few rides, and there is also an aquarium- which is MUCH smaller than Baltimore's, but is typically never crowded so what is there, is easily accessible. There is great outlet shopping, and a lighthouse you can climb (a good workout), and lots of "atmosphere" - the Boardwalk is sort of like Niagara Falls/Gatlinburg, with the little shops, restaurants, etc., and the casinos themselves have lots of good food options from fast food up to high-end gourmet. Other than aquarium and lighthouse, you can park your car and never use it (and often we will just cab to aquarium to avoid any driving)