Hi Linda,
The one site that spring to mind will be the CC club site at Stover, it's very near Newton Abbot, and a stones throw from Dartmoor via Bovey Tracey. We used the site about four years ago and although has basic amenities (no loo block) we found it more than adequate for a weeks stay. It's actually next to the Stover Country Park, so if you have a dog, this is ideal for exercise as the site only has a small dog walk. The site is also within walking distance from Trago Mills as well, the road is fairly busy but is reasonably quiet at night.
Hope this is of some use.
Wendy