I have answered a few similar questions recently and think they would apply here. The first one to consider is your rental company. Most have pretty good size lots and might be willing to accomodate your RV while you are vacationing.
In a previous post, it was also recommended to consider A-1 Towing Lot (252) 261-9777.
A final thought would be to contact one of the camp grounds in Kitty Hawk. Here is a link to the camping page to give you information on those possibilities.
Hope this helps. If anyone else has a suggestion, please chime in.