Myrtle Beach, SC is great if you like the typical busy beach atmosphere. There is so much to do there, you cannot possibly do it all. There is outlet shopping, a Medieval Times and other dinner theatre/shows, IMAX, water parks, permanent carnivals, a really nice aquarium, great restaurants, putt-putt, helicopter/airplane rides (some as low as $20 per person). You (and the kids) can get your pics with tigers (cubs or adults) and apes at Barefoot Landing. And, to top it off, MB has a really nice beach. One great place to stay is Dunes Village...it has an indoor water park.
The Outer Banks are fabulous if you want a slower speed! There is plenty to do there...go to see the Wright Brothers' Memorial, drive to see lighthouses (some you can go in), see the Nights In Rodanthe house (even though it has very recently been moved), climb the sand dunes and watch the hang gliders at Jockey's Ridge, watch the wind surfers near Hatteras, eat melt-in-your-mouth-good REAL seafood (although Calabash, near Myrtle Beach, has the best of all), go shopping, go offshore fishing, go to the aquarium, stroll the Elizabethan Gardens, explore the location of the Lost Colony - or check out nearby Jamestown, or you can just hang out on some of the most pristine (amazing) untouched & undeveloped beaches in the US (they even win awards sometimes for the most beautiful beaches in the world)---all with no huge crowds (in fact you can find beach spots with no one within sight)! There are not many hotels there (no high-rises to spoil the beach view); most people rent homes. You can also go a few hours south and stay in the Beaufort or Emerald Isle area...also very few hotels. Very laid back atmosphere and beautiful beaches. Beaufort has the maritime museum and claims to be where Blackbeard hung out. There is an island nearby with famous wild horses and daily boat trips to look for dolphins. In the Emerald Isle area (by the way it is a tiny island), you can see dolphins almost daily in the summer playing just past the wave break line.
The NC mountains are also nice. Tweetsie Railroad is fun for the kids. For the adventurous type, you can go whitewater rafting. It is easy to rent a cottage (for less than a hotel) or log cabin (or you can be brave and go camping)! Fishing there is fun! The Biltmore House is gorgeous (and impressive!). The gem mines, Grandfather Mountain, natural hot springs, hiking to the waterfalls...all awesome! This is a laid-back and very restful vacation spot with gorgeous scenery. The NC mountains is where they filmed much of Dirty Dancing and Last of the Mohicans...you can visit the movie sites. In the far western part of the mtns (near the TN border) you can take a train ride that goes past the site where they filmed a bus/train wreck for The Fugitive...all the wreck is still there.
I also love Washington, DC. If you stay just outside the city and are willing to ride the metro in (some kids think that is actually an extra bonus!), you can find a great deal not far away from the action. Crystal City (in Arlington VA) is a great place to stay, and the metro ride in is easy! All the Smithsonian museums are FREE (a great added bonus!), including the zoo! You can check out the White House, lots of memorials, Arlington National Cemetary, a wax museum, the Ford Theatre (where Lincoln was assassinated), even the train station is lots of fun (my DS8 is a huge train fan, so many of our trips revolve around trains!). Washington DC is not too terribly far from Richmond, VA, where there is an amusement park (King's Dominion), so if you want a 1-day fix, there you go...they have great coasters for big kids!
You could also consider a trip to the Caribbean. Believe it or not, you can find great deals that make it very affordable without giving up luxury or security! We go to the Caribbean every single summer (either by cruise ship or staying at an All-Inclusive Resort) and it is heaven!
I am a teacher in NC, and I LOVE to travel!! Every summer, my kids and I get in the car and head to these places and more (and, by the way, I feel safe even on my own with just the kids in each of these spots). The kids love to go just like their momma! This summer we will be going on a cruise to the Caribbean, will spend a week in Emerald Isle for July 4th, will spend at least 2 long weekends in Myrtle Beach, and I am considering either New York (another great idea...shows, shopping, big buildings!, Central Park, maybe even a side trip to Niagra Falls) or along the coast of New England for lighthouses and historical sights (I teach literature...lots of cool stuff up there for literature lovers) or maybe even just drive to see the Mississippi River (I know...seems weird...I just want them to see it & put their toes in!).
I got incredibly long-winded...I'm thinking of becoming a travel writer (focusing on travel with kids), if I can find an outlet. If you need any details....just ask! Have fun planning!