Thinking about it... it is the opposite side of Stonehaven from the castle, but if I was looking for a wild pitch close to Stonehaven, I would head down to Skatie Shore, where the Highland Boundary Fault hits the North Sea.
You head out of town past the golf course and under the railway line until you come to a parking area/turning circle at NO 883877. Across the road a path heads through some woodland and then heads back towards the sea under the railway viaduct at NO 888880. Once you hit the shore, turn right back towards Stoney and there are a succession of attractive bays with a wide grassy area above high water which would make a great area to camp. You would probably want to bring fresh water in with you though, there aren't many streams in the area.