you can camp on any of the open moorland on dartmoor (except for MOD firing range land, which is marked on OS maps), any private;y owned land you need permission to camp on obviously, there are a few pleaces you are not allowed to camp.
You basically won't find anywhere to camp with trees that is not privately owned... so your only options are campsites or open morrland.
Considering the size of dartmoor you will always be out of the way! lol
Dartmoor can also change at a minutes notice so check the weather forcast befor going.