Coming out of Ashburton just past the road to Holne, over bridge then park on left hand side in car park at Newbridge, there is a Dartmoor National Park office there.
If you walk along the river that side of the road there are plenty of places to camp.
I like a place called Blackstone on that side of the river, bit of a hike as you have to hug the river but well worth it.
For an easy stay, cross the road from the car park and walk to Spitchwick, a Ten minute walk, people camp there and it's a good place to swim, good for families as well.
I used to walk up the hill from the car park for exactly Two miles to the Tavistock Inn, the first time I did it I forgot to take a torch with me, when I left the pub a Ten thirty it was pitch Black, it took me ages to walk back safely.
I love that place been there loads of times.
Edit, Just saw Jacknife's post before posting this, same place.
Enjoy your stay.