@Useafortyfive The Fed sid of the park is great is you have a 4x4, when you get your permit (a little over $100) it's for a year, no week or day passes available. You also need to pay a fee to enter the park area (day fees are available but the annual pass is fairly cheap). The day permit allows you to stay on the beach till midnight.
There is air available when you get off the beach to air up your tires (it's free and there are several hoses).
There is also a list of equipment you need to have with you. It's pretty standard stuff if you offroad, and the list is on their website in the rules.
Get onto the beach and drive down about 10 miles and there are few (if any) people around. Great area for sunbathing, surf fishing, and such. If you want to actually swim watch out for the undertow it can be really strong in that area.
ETA: the other 'cool' thing to see is a bit further south on the VA side - Chincoteague Island. There is a NASA facility nearby (Wallops Island) where they do occasional launches including support missions to the ISS (check their website). They have a visitors center that is decent on 175 just before you get to Chincoteague Island.