And which town do you recommend?

Midweek, early September. Lower rates, much thinner crowds, surf still warm enough to swim. Duck or north of Duck, or Rodanthe or south of Rodanthe.

When our kids were smaller we always went to the Outer Banks as soon as school was out and went camping on the beach. Water warm enough and not crowds.

I once drove from Boston to the OBX on the Saturday of Labor Day weekend. We arrived Sunday morning and the place was emptying out. Many of the hotels were lowering their summer rates because the tourist season was over. We stayed in Kill Devil Hills at a little cheap motel right on the beach for something like $35 a night. The resturants were open, the weather was beautiful and the water was so warm!