Is there a cost for camping

Fees vary due to if they are primitive, standard, full or partial utilities plus there is an additional fee for the required discovery pass

There are campsites within the park. $11 per night

I believe the only camping allowed is not actually in the park. There are spots at the inn at the entrance if memory serves. The park requires the Discover Pass which costs ten dollars for one day or thirty for the year. I got the yearly one. It's good for any state park.

Or you can pay 10 bucks at the ranger station at the bottom. They have a machine to pay and get a pass outside. Super easy.