We have gone to Va Beach in September for the last several years an think that it can be the best time to be there. The weather is usually still swim weather. Last year was the exception being cool and cloudy most of the week.
We always stay at Holiday Trav-L-Park. I don't know how it is for the neptune festival, but earlier in the month the campground has relatively few campers. Plenty room for privacy. I would suggest you give them a call and ask about that week.
We went to Va Beach accouple of years ago. The Holiday Trav-L-Pak was great. We went in June (little cool). (one day day was a total rain out do to the huricane that come up from FL) It did flood out the front section for the tent campers and just so you know the rest of the park was dry. The sites are nice and if you want they have a newer section with concrete pads. We had a great time.