If you are on Beach Rd then you will have a long walk/bike pathway for the kids to ride their scooters. I have ridden my bike from South Nags Head (mp 19) clear down to Kill Devil Hills (mp 9). I have seen people using the path for walking, jogging, biking, skateboarding, in-line skating. I don't remember seeing scooters but I'm sure they would be fine. We love that area.
Incidentally, if you love pizza and good italian food, please try New York Pizza Pub in Nags Head. Oh my gosh is it ever delish!! In a typical week, we go at least twice.