K.M.
We have gone to the Outer Banks off the coast of North Carolina for the last 3 years and highly recommend it. We go with friends (including 6 kids under the age of 4). We rent a house right on the ocean with a private pool and beachfront access. It's very relaxed and fun for the kids. We also like be in a location where we can walk to the main shopping area. We stay in Corolla, but there are many great places to stay depending on what you are looking for (Duck, Kitty Hawk, etc.)
Here's a couple of rental websites:
http://www.corollaclassicvacations.com/
http://www.twiddy.com/
Note: rental costs vary significanly depending on what time of year you go.