Is ok to spend a night in the woods here?

Yes. They have tent sites and camper sites, as well as, cabins.

There is a campground a few miles up from the water and beach. Its fairly inexpensive too. Cabins I believe are $50 a night.

There is a camp ground and a remote site that you need to reserve early. As far as just sleeping anywhere it is not permitted and renters will go looking for you if they see your car in the parking lot.

I agree with Chuck.